Solving a tricky SAT square root problem
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- Опубліковано 3 сер 2024
- How do we combine square root numbers? Here we will work out the square root of 20 minus the square root of 5, i.e. sqrt(20)-sqrt(5)=? You need to know how to simplify square root numbers and how to combine square root numbers for your algebra class! Subscribe to @bprpmathbasics for more algebra tutorials.
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0:00 sqrt(20)-sqrt(5)=?
4:21 You try sqrt(18)-sqrt(8)=?
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#math #algebra #mathbasics
Can you solve 2^x=5^(x+2)?
Answer: ua-cam.com/video/WL-npSEyVTo/v-deo.htmlsi=wYnDM4fJ3u9ROqRo
Thought Process:
sqrt(20) = sqrt(5 x 4)
sqrt(5 x 4) = 2sqrt(5)
2sqrt(5) - sqrt(5) = sqrt(5)
Yeah takes like 2 seconds hahah
And I thought I m doing some mistake since you can't get answer so easily
Same 👍
Thx
Easy
Huh! It was easy, I solved it right away!!
me 2
Good. Have a gumdrop.
Dweeb
@@TheBatugan77 mad cuz he’s good at math? Enjoy hell
ikr this ain't tricky
@@TheBatugan77 bruh has never taken algebra lmfaoooo
(√18)-(√8) is
(√9*√2)-(√4*√2) furthermore
3(√2)-2(√2)
Radicals are same so we can subtract it,right
So 3-2=1 Then,
1(√2) or simply (√2)
ua-cam.com/video/cH0yvkYT1CU/v-deo.html
for me, i did
sqrt(18)-sqrt(8) is
(sqrt(9)*sqrt(2))-(sqrt(4)*sqrt(2)) that is
sqrt(2(sqrt(9)-sqrt(4))) that is
sqrt(2(3-2)) that is
sqrt(2*1) that is
sqrt(2)
@@7MinutozRapsLetrashey could you help me understand the step of
sqrt(2(sqrt(9)-sqrt(4)))
I don’t understand how you got there from
(sqrt(9)*sqrt(2)) - (sqrt(4)*sqrt(2))
@@marquis5178 im sorry this was almost a year ago and i dont remember my own maths 💀
Wait i remember
So, when you have, lets say sqrt(4)
You could do sqrt(2)*sqrt(2)=sqrt(2*2) = sqrt(4)
Basically, its sqrt(x*y) = sqrt(x)*sqrt(y)
@s5178The problem is partially due to a typo problem: when 7MRL typed _sqrt(2(sqrt(9)-sqrt(4)))_ they probably meant _sqrt(2)(sqrt(9)-sqrt(4))_ i.e. they got the shared factor _sqrt(2)_ out of the parentheses.
And because _sqrt(9)-sqrt(4)_ is 1, the equality's stayed correct, despite the typo braking down the reasoning.
Answer to hw question √2
1 + 1
√2 = 1,414...
@@florinpichiu691 *1.41
@@Baconindamorning You're right, but I personally prefer using three numbers after the comma, just to be more specific.
Because it's 3√2 - 2√2
3√2 - 2√2 = √2
This man explained it so well, but it didn't have to be so lengthy. This could've been done by prime factorization and grouping the factors into groups of two.
He did explain it well, especially for those who can’t remember the factors.
ua-cam.com/video/syWx6dwWa-M/v-deo.html
@@bettygilliland456 Prime factors don't have to remembered in general, just the rules for divisibility for small primes (mainly 2, 3, and 5). Successively applying that (or doing a little more work for higher primes) gets you the factorization.
@@bettygilliland456You don't need to remember anything to factor 20. In fact if you can't factor 20 you should not be doing this problem.
Math is not about "know how to solve a problem". It's all about "find the solution yourself".
If you lack some critical skill that is needed for this level of problem, it's better to consolidate that first.
Hey yahtzee...
SHOVE your lengthy.
My approach:
Let the whole equation be x, and square both sides
then we have (sqrt(20) - sqrt(5))^2 = x^2
20 - 2 * sqrt(20) * sqrt(5) + 5 = x^2
20 - 2 * sqrt(20 * 5) + 5 = x^2
20 - 2*10 + 5 = x^2
5 = x^2
x = sqrt(5)
That's it
Why?
Just take sqrt of 5 out, 2-1=1 and get sqrt of 5.
@@Yesytsucks what?
@@diamondsky3787 root 20 equals 2 root5 so it is 2 root 5 - root5= root5
@@Yesytsucks everyone has different approach. Even i did it like him.
@@premnath2333 congratulations, you waisted a lot of time on a two step problem
You can also do it this way. If you notice that the radicands multiply to a perfect square, solve it algebraically by squaring both sides. So initially, the problem is sqrt(20) - sqrt(5) = x. When squaring both sides, you end up with sqrt(20)^2 - 2*sqrt(20*5) + (- sqrt(5))^2 = x^2. This yields 20 - 20 + 5 = x^2 or 5 = x^2. We know the solution is positive since sqrt(20) - sqrt(5) is positive, so we can ignore the negative solution to this quadratic, so the solution is x = sqrt(5).
Note that sqrt(144) is 12 or -12. I used 12, not sure how to justify throwing away -12, which would leave us with sqrt(50) = x.
Regarding the original problem, it is _not_ true that sqrt(20) - sqrt(5) is positive:
sqrt(20) - sqrt(5) = -4.47 - 2.236 = -6.7
@@daapdary while it is true that given x^2 = 20, x = +- 2*sqrt(5), the notation sqrt(x) assumes the positive result only. It's convention. That's why if you plug x = sqrt(20) into wolframalpha or sqrt(20) into calculator, it will only give the positive value.
@@theeternalsw0rd Good point, thanks! So, sqrt(144) is positive in my example, but if I had started with 144 and then took the square root, it would be ± sqrt(144). The convention makes sense: a square root _function_ (where the domain is nonnegative real numbers) might as well return the nonnegative square root.
That's exactly how I did it. Was about to comment but found yours...
This is a nice trick to know. Back in school I used to just put everything into a bracket and multiply it with itself so it would be something like (a-b)^2 which equals a^2 - 2ab +b^2 and then apply square root to this result; this way you get rid of the square root and ab would always give you a perfect square. If ab is not a perfect square this technique wouldnt work but neither would his.
Thought process:
2 is the square root of 4, so the square root of 5 is close to 2.
4 is the square root of 16 but since that is a bit further away from 20, changing the number to 4.5 is a bit over 20 so that works.
4.5 - 2 =2.5
Now since the answer asks for a square root, that number must be squared.
2.5 × 2.5 is around and closest to 5.
Final answer: square root 5.
That's what I thought at first as well but its not quite accurate I guess
Not that complicated , sqrt20 is the same thing as 2sqrt5 - sqrt5 answer is very simply and easily sqrt5
I thought in the same way as you.
solution by me : square root of 20 : 2 root 5. now 2root 5 - root5= root5(2-1) {taking root 5 as common} => root 5 x 1 = root 5.
2.5 x 2.5 is 6.25. Not really close to 5
Learned something new today, thank you!
Calculated before seeing video and got it right...
This is the kind of problem that seems tricky when you first glance at it, but is trivial when you think about it for a few seconds. It is ironic how things can be that way, that what you think is tricky is really simple, or conversely, what you think is simple is really quite tricky.
@UCxNMlPEiqKVeZZ6I8q_nJww There are some high-school students where I would be relieved if they could find the state that Chicago is in, on a map of the U.S., or tell you what year that the War of 1812 took place. So am joyful if they can solve this little math problem easily, which I am sure some can, and by rights, most of them should be able
@@tom-kz9pb When I first read that, I was doubted you. Then I remembered my classmates.
Why is every SAT math question i see always so easy
Great explanation! :)
sqrt(1.6)+sqrt(0.9) = ?
(A) 0.7 (B) 0.5 (C) 7sqrt(10)/10 (D) sqrt(10)/2
Answer here: ua-cam.com/video/PWCx_dVs4xk/v-deo.html
Muito boa a aula!. Abraços professor.
I like your work very much. I've already counted a few. Keep it up.
A thumbs up from me for that...thank you
You're a intelligent person .
Many thanks
Easiest questions i have seen in years 🙂
The other way to do it without recalling the mathmatical relationhship of breaking out a square root under the radical is:
Simply estimate the square root of 20 which is between 4 and 5...let's call it 4.5.
Then do basic square root of 5 in your head and say that is ~ 2.2
Perform 4.5-2.2 = 2.2 or 2.3 and square it...again in your head = 5
So answer is square root of 5. This is made possible by multiple choice doing basic arithmetic in your head aka deduction.
Of course, the mathematical answer is pretty well known as well for people that passed math class and I have had a lot of calculus so not a big deal...lol.
thought process:
A = sqrt(20) - sqrt(5)
A^2 = (sqrt(20) - sqrt(5))^2
We can use a^2-2ab^-b^2
sqrt(20)^2 - 2 * sqrt(20 x 5) + sqrt(5)^2
20 - 2 * 10 + 5
A^2 = 5
sqrt(A^2)= sqrt(5)
mine seem to be different from others
abit excessive but it works
@@DylanKJW yea i wanted to be a little different lol
@seo-woojin lol that's what I did too i only know irrational equations so I did it like that
@@tzbq lol i forgot this vid one year ago 😂 seems i have gotten some likes and never knew
Too easy! Thanks!
Sqrt(18) - Sqrt(8)
(Multiply everything by root 2)
=> {Sqrt(36) - Sqrt(16)}/(Sqrt(2)
= (6-4)/Sqrt(2)
= 2/Sqrt(2)
=> Sqrt(2)
This method is satisfying
Nice video! I wonder how you came up the option of sqrt(2.5) 🤔
Love Algebra and Calculus (especially Green’s, and Stoke’s Taylor’s Theorem) and differential equations!
You are a genius!
I just did a bunch of aproximations and got it wright from that
Edit to explain. I knew that square root of 20 would be a little under 4.5 (after checking work later its 4.472)
And i knew square root of 5 is under 2.5 but i knew it was more under 2.5 then the other number was under 4.5 so wighted it by making it 2.3. 4.5-2.3=2.2 thus logically square root of 5 was the closest.
I did it a little more complicated
Say / means Sqrt (easier to write)
/20 - /5 = x
(/20 - /5)² = x²
(/20)² + 2(/20 × -/5) + (/5)² = x²
20 + 2×-10 + 5 = x²
20 - 20 + 5= x²
5 = x²
/5 =x
My method :-
We begin by taking the square of the expression.
(√20 - √5)^2
= 20 + 5 - 2 ( √100) [ By using the formula = ( a - b)^2 = a^2 + b^2 - 2ab
=20 +5 - 2(10)
=25-20
=5
= If, (√20 - √5)^2 = 5, then
= √20 - √5 = √5
Impressive ❤️
oh damn, i really thought this was a trick question with me double guessing my answer of sqrt(5) because it was called a tricky SAT question. But it turns out that it was just a normal question.
My try before seeing: sqrt(20) can be written as sqrt(4) x sqrt(5)
So our expression now is
sqrt(5)*sqrt(4) - sqrt(5)
Factor out sqrt(5)
sqrt(5) ( sqrt(4) - 1)
sqrt(5) ( 2 - 1 )
sqrt(5) (1)
sqrt(5)
Hope am correct
same
Ye or I mean sqrt20 is just sqrt4 x sqrt5 which is just 2 sqrt5
2 sqrt5 - sqrt5 = sqrt5
You are correct but you took such a long route
@@finnwilde This was my thought too xD
Hablo español, pero me gusta ver todo tipo de vídeos sin importar el idioma, porq entiendo los ejercicios a pesar de todo
ua-cam.com/video/syWx6dwWa-M/v-deo.html
Wachate los videos en chino
Wait wha- no way, a video from this guy that's actually easy
This is SAT hard questions. WOW!!!!
4:26 (√2)
sqrt(20) is something between 4 and 5, sqrt(5) is something between 2 and 3, so subtracting the two should give you something pretty close to 2.
sqrt(15) is almost 4, so that's out.
sqrt(10) is more than 3, so that's out.
sqrt(5) is between 2 and 3, so a possibility.
sqrt(2.5) is less than 2, so that's out.
Only the square root of 5 is in the expected ballpark, so that's gotta be it.
That's how I did it
@@katieevans6017 Me too! This approach had a nice *feel* to it.
Why wouldn’t you just do the problem? You can do it easily in your head. No guessing needed.
@@ES-hr6vg Because the idea of factoring the radicand doesn't always occur to some of us ;-) All the more so in a case like this where the numbers involved are all small enough that the closest perfect squares are trivial enough to do the estimations indicated.
@@sststr really? But factoring whatever you can wherever you can is generally best practice lol
Another thought process
In this case, we can think with bounding the values.
Now that the perfect square roots are written down, you can evaluate that 4 < sqrt(20) < 5, and 2 < sqrt(5) < 3, so the answer is roughly 2, which in this case only corresponds with sqrt(5).
In tests like SAT, where you are given answers to choose from, and not specific values, this can be nice to use.
This can also help in general when you need to estimate the value of a square root, like sqrt(55) would be between 7 and 8.
Edit: for the bonus question, sqrt(18) is slightly above 4, and sqrt(8) is slightly below 3, so the answer would be slightly above 1, which in this case is ~1.4 = sqrt(2)
Nice one
root(18) can be written as 3(root2) and root(8) can be written as 2(root2)
so it is 3(root2) - 2(root2) = root(2)
You could've also taken the whole square as (a - b)² = a² - 2ab + b²
And the square rooted the answer
Square 2, thanks for learning
Such an easy question
As an Indian 9th grader this was not that tricky rather I think it's one of the places where i can easily score good marks
the biggest challenge with sat is the reading part
Damn that's relatable, solved it without breaking a sweat
You shouldn't be proud,in India we are doing much greater things than this in class 9
@@ts9dream in India do you do calculus I and II in 9th?
I agree
The simplest method I came up with, to solve √20 - √5 = ?
[√20 = 2√5(you can get it by factoring method)]
(Since we can write 2√5 = √5 + √5)
Now,
√5 + √5 - √5 = √5 (cancelling or subtracting √5 - √5)
So the answer is Option C) √5
As someone jumping back into school after a 3 year break i enjoyed being able to pause and solve on my own!! I feel a little proud remembering how to do that one
This is a super easy question 🤣 I felt like if the title was a click bait 😂🤣
For the tryout question, the answer is "D", square root of 2.
Square root of 18 is the same as 3 root 2, and square root of 8 is 2 root 2.
3 root 2 - 2 root 2 gives you root 2.
my thought process:
root 25 is 5 so root 20 will probably be 4.something
root 5 is probably about 2.5
4.something-2.5 is likely around 2.5
the only one that's around 2.5 is root 5
Are you an engineer by any chance?
ua-cam.com/video/syWx6dwWa-M/v-deo.html
ua-cam.com/video/cH0yvkYT1CU/v-deo.html
At first i was like i have no clue but then i opened the video and when he said try it yourself i was instantly like ”yeah i remember how this is done” and got it right in a few seconds
Man its a very easy concept about squares surds and rationalisation of surds
What I want to know is why he is holding a Poke' ball, with no reference to it at all. Is it his eraser? Maybe it it to catch new subs. "Gotta cetch 'em all!"
@@bprpmathbasics Ahhh, clever, but, is it a mic or a mic muff? I would put it on a mic stand or boom stand and tap it a couple of times with you pencil at the very beginning and say "Is this mic on?" even though you know it is. It's a common show-biz reference. Then you don't have a distracting element in your presentation.
I imagine that you can't draw too much attention to it or say "Gotta catch em all" or the like for trademark issues. ORRR you could say something like "Don't miss any of my lessons, gotta catch em all" and have that be part of your shtick. Consult your attorney on that one though. ;-)
sqrt(20)
=sqrt(5 x 4)
=sqrt[5 x (2^2)]
=2sqrt(5)
2sqrt(5) - sqrt(5) = sqrt(5)
Literally takes like 5 seconds if you know your squareroots
same i thought
take sqrt20 - sqrt5 equal to x
take square on both sides solve for x sqr
then take square root on both sides
and answer is sqrt5
I have a good and very simple method for my students.
If we want to add or subtract any two square roots, we need to use two rules.
(BTW, we can do that with any square roots in a "good-looking" expression or a "bad-looking" one.)
√A+√B --------------------------- √A - √B
1st rule
"ANY DIVISOR?"
We are able to do a such math operation (by the nice way), but only if
A is the divisor of B or B is the divisor of A or we have the HCF of A and B bigger than 1.
So
√15 - √8
above expression we can't simplify ("nicely"), because we dont have any divisor there and no HCF (bigger than 1) either.
2nd rule
"DIVIDING RULE"
If we found some divisor of A and B or their HCF, we can use this procedure
√45 - √5
just divide 45:5 = 9
then
√9*√5 - √5 = 3√5 - √5 = 2√5
This is our "good looking" expression.
The bad-looking expression (but, of course, we don't use that way, however, sometimes it could be usefull):
√30 - √5 -----------------------> 30:5 = 6
√6*√5 - √5 = √5 (√6 - 1)
If we have the case like that
√18 - √8
we must use the HCF -----> HCF = 2
18:2 = 9 -------------------> 8:2= 4
√9*√2 - √4*√2 = √2 (3-2) = √2
The case with a "bad-looking" expression (but, of course, we don't use that way, however, sometimes it could be usefull):
√15 - √6
we can use the HCF -----> HCF = 3
15:3 = 5 -------------------> 6:2 = 3
√5*√3 - √3*√2 = √3 (√5 - √2)
Another method (more satisfying)
Multiply everything by square root 5
That gives - square root 100 - square root 25/ square root of 5
Which then gives - (10 - 5)/ sqrt(5)
=> 5/sqrt(5)
=> sqrt(5)
pretty nice
(SQRT 20 - SQRT 5) =
SQRT 5 × (SQRT 20 - SQRT 5) / SQRT 5 =
(SQRT 100 - SQRT 25) / SQRT 5 =
(10 - 5) / SQRT 5 =
5 / SQRT 5 =
(SQRT 5 / SQRT 5) × (5 / SQRT 5) =
(5 SQRT 5 / 5) =
SQRT 5
extremely over-the-top lol, takes too much time and opens up the possibility to make a mistake during the calculation
Все легко, просто приблизительно от корня 20 получаете 4, а от корня из 5 - 2. 4-2 = 2 и дальше уже выбираете самое близкое значение 😄
Ну, если в конце эту 2 возвести в корень, те √4 то да
Не знаю зачем возиться с приближениями, когда можно 30 секунд потратить и получить ответ как в видео
ua-cam.com/video/syWx6dwWa-M/v-deo.html
ua-cam.com/video/cH0yvkYT1CU/v-deo.html
√18 - √8 = ?
(√9 • √2) - (√4 • √2)
3(√2) - 2(√2)
If ax - bx = (a-b)x
then answer is D, √2
omg i learned something im so proud
THANK YOU 🧠🙏🏻
I like how this is just basic surds
While actually knowing how to multiply/factor roots is easier, the multiple choice question does not require that. Root20 is between 4 and 5, say around 4.5 (20 being between 16 and 25). Root5 is 2 and change (5 being slightly bigger than 4 but significantly less than 9). So 4.5 minus 2 and change is going to be 2 and change. Root15 is going to be bigger than 3, throw that out. Root10 is also bigger than 3, throw that out. Root2.5 is less than 2, throw that out. Root5 is what's left.
ua-cam.com/video/syWx6dwWa-M/v-deo.html
I nailed that one in a matter of seconds, but the SAT isn't really hard, nor is the ACT, and they aren't supposed to be. They show objectively whether you learned anything in high school, and I love them for that. It doesn't matter if you brought something for every "teacher appreciation day".
but GCSEs and A-levels tho in uk
A note for test takers: to save time, treat the radicals like units or variables. Usually the answer will be the one that is in the same "unit." In the original question, we know that radical 5 will be the unit, so the answer has the contain a radical 5. For the second question, once we reduce radical 18 and radical 8, we are left with "units" of radical 2. The only answer choice with the same "unit" is D.
I looked at the thumbnail and solved it in less than a minute. It's really not that bad, it was easier for me cause I've been doing some review on this before school starts and may be more familiar with this at first glance. Otherwise, I don't see why it would seem like a hard SAT question.
root 20 = 2 root 5
2 root 5 - root 5 = root 5
Answer √2
Procedure:
√18 - √8
We brake down √18 = √2*√9
And √8 = √2*√4
√9 = 3
√4 = 2
So we have
18 = 3√2
8 = 2√2
3√2 - 2√2 = 1√2 = √2
Hope it’s clear.
E você está certo! A decisão certa é surpreendente!
The moment u realise that √20 is 2√5
You rub ur nose on wall
Using his method on the second equation, you can break down the sqrt(18) into sqrt(9)*sqrt(2) (you can also break it down into 3 and 6, but they aren't perfect squares, so they're not helpful) You can also break down the sqrt(8) into sqrt(4)*sqrt(2). Both 9 and 4 are perfect squares, so you end up with 3*sqrt(2)-2*sqrt(2). It becomes a simple case of 3-2=1, and you're left with sqrt(2), making the answer D.
Better way, square the whole equation. That is 5. Then take root, that is √5
This also relies on the fact that you must make the expression contain roots of perfect squares only
@@ATeima-kk5ps kind of luck. But I works for sure
@@anirudh7455 no i didnt say the solution luckily worked for you, i just said that its not "better" than his solution. Still a good solution though
👍
@@ATeima-kk5ps I actually worked this way because I looked at the options and their square would be a whole number.
@@anirudh7455 yeah it is a nice solution
I just estimated
sqrt20 is 4.5 and sqrt5 is 2.
4.5 - 2 = 2.5
2.5 ^ 2 is roughly 5 therefore the answer must be C.
same
We can see that sqrt(20) is between 4 and 5, and that 20 is 4 more than 16 but 5 less than 25, putting it at approximately 4+4/9, or 4.44.
And, we can see that sqrt(5) is between 2 and 3, and that 5 is 1 more than 4 but 4 less than 9, putting it at approximately 2+1/5, or 2.2.
If you want a formula for that, it's LB + (MT / (MT+LT)), where:
LB = The lower bound of possible values.
MT = The "more than" value, or how much more the parameter of the function is than the square of the lower bound.
LT = The "less than" value, or how much less the parameter of the function is than the square of the upper bound.
It's only an approximation, but it's more than enough to do a multiple choice question like this in your head.
In the case of sqrt(20), LB = 4, MT = 4, LT = 5, so we get 4+4/9.
In the case of sqrt(5), LB = 2, MT = 1, LT = 4, so we get 2+1/5.
Thus, sqrt(20) - sqrt(5) is approximately 4.44 - 2.2, or 2.24, which is incidentally the exact value of sqrt(5) to 2 decimal places, so it's pretty safe to say the answer is C.
EDIT: Oh, and applying this to the bonus question:
sqrt(18): LB = 4, MT = 2, LT = 7, so it is approximately 4+2/9, or 4.22
sqrt(8): LB = 2, MT = 4, LT = 1, so it is approximately 2+4/5, or 2.8
Thus, sqrt(18) - sqrt(8) is approximately 4.22 - 2.8, or 1.42, which I probably don't need to tell you is pretty darn close to sqrt(2), so the answer to that is D.
For an SAT question this seems very easy lol. I was taught how to do this in 8th grade
For the ending question
sqrt(18) - sqrt(8)
=sqrt(9) × sqrt(2) - sqrt(4) × sqrt(2)
=3 × sqrt(2) - 2 × sqrt(2)
=sqrt(2)
Thought process
Sqrt 20- sqrt 5
= Sqrt 5 ( sqrt 4 - 1 )
= Sqrt 5 ( 2-1 )
= Sqrt 5 ( 1 )
= Sqrt 5
E você está certo! A decisão certa é surpreendente!
Haha, what I did was:
2√5-√5=2 😂
But since in the answers there was no 2. I changed my approach and got √5.
I did it like that too bro 😢
5min of video for 5 seconds of 5h grade math...
Sqrt18-sqrt8
Sqrt (9*2) - sqrt (4*2)
3sqrt 2 - 2sqrt 2
Sqrt 2
Answer D
i did a digit-by-digit estimate in binary and found sqrt(20) was exactly double sqrt(5). its pretty obvious there; since four is one of the factors of 20, it appeared in the binary representation with a pair of zeroes, which had the effect of shifting everything one bit leftward in the root, AKA multiplying by 2.
The difficulty of the problem comes not from my own math abilities, but my own doubt in my math abilities. I legit got C in like three seconds, but I continued to second guess myself for minutes on end.
Idk if anyone else did it my way but it was pretty funny:
=> √20 - √5 = x
=> 2√5 - √5 = x
=> (Factor out √5), √5(2-1) = x
=> √5(1) = **√5 = x**
Your questions have taught me to square both the sides
ua-cam.com/video/cH0yvkYT1CU/v-deo.html
thanks!!!!!!!!!!!!!!!!!!!!!!!!!!!
What I did was square the entire equation and then when I got five as the answer I took the square root of that :)
The fact that SAT questions are this simple tells you how easy it is for Americans to get into Ivy Leagues.
Man i learned it in 8th grade and that question was one of the easy ones it was the first ever equation with square root ive ever done, like there are equation that are 100× more vomplicated
I just did it by approximation. 4^2 and 5^2 are 16 and 25, so sqrt of 20 should be around 4.5, apply same logic to sqrt of 5 and you get around 2.2, so the answer is approx 2.3. srqt 5 seems closest to 2.3.
The multiple choice answers also make it way too obvious, since 15 and 10 are bigger than 3 squared and 2.5 is smaller than 2 squared. Sqrt of 5 is the only one that's even in the ballpark.
The thing I always do is breakedown in numbers every sqrt to compare the results
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Easy but nice one
You can do (/4 x /5)- /5. And since /4 is 2 it would be 2/5, then 2/5 - /5 = 1/5 therefore it’s /5
sqrt(18)-sqrt(8) = sqrt(2)
Good video
Btw guys if you're not in algebra yet the thought process won't be as difficult as this he's just explaining the main idea of the question
I solved it in my head but a little bit different, I’m not sure if I just got lucky though.
I multiplied (sqrt20 - sqrt5) by sqrt5 and got sqrt100 - sqrt25 and they simplify to 10-5 which led me to pick c
Edit: I did the same thing for the last problem but multiplied sqrt18 - sqrt8 by sqrt2 and got sqrt36 - sqrt16 which simplifies to 6-4 which is 2, so option D
4:20 Oh! I get it😲When you split the sqrt the sqrt of 20, you then do that to the sqrt of 4 BEFORE YOU DO ANYTHING ELSE. Then multiply that by ONE of the two sqrts of 5, and then subtract the OTHER one. Better remember that if I can get back into College Algebra.🙏🏻
I did solved this type of questions in 9th.
The answer of the hwk is √2 option {d}.
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Can be done more easily by (a-b)² = x²
Where x is the answer
D as answer for the given question
C) 2(5)½
Very easy solved in mind🙃
you could also factor sqrt5 out of 2sqrt5-sqrt5
=sqrt5[2(1)-1]
=sqrt5(1)
=sqrt5
That is so easy bro
Thank you for this! I knew how to do it, but I'm glad that I was able to remember, but the real people who needs help is my brother. Math isn't his think and his Algebra teacher didn't really teach well, so I may send this to him! :D
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