@@dhruvsantra9027 because 58 is 8 away from 50. this trick revolves around 50. 42^2 for example would be 8 away from 50 and 8^2 is 64, 25-8 = 17 so 1764
Since this trick only applies to perfect squares, could you tell me how do I find out whether the number is a perfect square or not without the need to taking the square root of it, please?
Prime factorization. If you can express the number as a product of prime factors in which there is exactly an even amount of each prime factor, or, in other words, when expressed in exponentiation form, all the exponents are even, then the number is a perfect square. For example, the prime factorization of 900 is 2 x 2 x 3 x 3 x 5 x 5 or 2² x 3² x 5². Since all the powers are even, then the number 900 is a perfect square. This is because 2² x 3² x 5² = (2 x 3 x 5)² = 30². If you get the prime factorization of 500, that would be 2 x 2 x 5 x 5 x 5. This is then written as 2² x 5³. Since there is an odd number of 5s being multiplied, 500 isn't a perfect square. Infact, if you take the square root of 2² x 5³, you are left with √(2² x 5³) = √(2² x 5² x 5) √2² x √5² x √5 = 2 x 5 x √5 = 10 x √5 = 10√5. In short, find the prime factorization of the number. If you can group all the factors into pairs, without any left over, then the number is a square. In fact, if you can group the prime factors of a number, in to groups of "n", then the number is a perfect nth power. For example, if you take 1728, and find the prime factors, you will get 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3. If we group these into pairs, we will get (2 x 2) x (2 x 2) x (2 x 2) x (3 x 3) x 3. Since there is an extra '3' that isn't part of a pair, 1728 is _not_ a perfect square. _However_ we can group these into 3s: (2 x 2 x 2) x (2 x 2 x 2) x (3 x 3 x 3). This means that 1728 is a perfect cube (power of 3). In this case, if you take one number from each group, and multiply them, that is your cube root (i.e. 2 x 2 x 3 = 12).
Ex: sqrt of 926 You just need to know some numbers like 10×10=100, 20×20=400, 30×30=900 and so on You get the the number 30 forward and multiple then by thenselfs 30x30=900 31x31=961 So its about 30,5 or less,this part you calculate by hand to be easier I hope yall get it,cuz it helps a lot 😅
It's a nice trick, but one small quibble. You started off saying you only need to learn the squares of 0 through 9, and you end by casually throwing in the square of 12.
Well finding the square of 12 is definetly better than finding the square root of 15876 (if it was possible without using this method) so i don't think its a big deal to complain about it
@@Bruh4502hi. Well, I wasn't actually complaining. I think it's a nice video, and I like nifty maths tricks like this. You have to admit, though, that he did start off saying you only have to know squares up to 81, but within a few minutes he'd moved to, you all know the square of 12 is 144. My comment was really meant in a light-hearted way.
There is no way most people would be able to pick the number(s) who's square ends with the same digit as the square we're trying to find the root of, then remove the last two digits of the answer, then find the number who's square is less than the remaining part of the number without the last two digits, then multiply that number by the next number, then choose the greater of the two possible last digits, if the original number is greater than the number we got by multiplying the number who's square is less than the part of the number we got by removing the last two digits..... in 3 seconds. Also, if the difficulty of a task is unrelated to the time it takes to do a task, then another way of finding the square root of a number, is the use of prime factorization. For example, for 3364, we will find the prime factorization: 3364 | 2 1682 | 2 841 | 29 29 | 29 1 Now we simply write the product of the numbers in the second column, like so: 2 x 2 x 29 x 29 To simplify this, we can then rewrite this expression in the form of exponents: 2² x 29² Then we can simply take the square root of this product, to find the answer is 2 x 29 = 58.
Hey thanks for this But how we remove the square roots in the last step? -does 58 have to get simplified -does 58 have a square root? -what do we do with 58 then?
@@Uninspiredz Um.... you are aware that 58 _IS_ the square root, right? If you're asked to find the square root of 16, and you get 4, what do you do with the 4? Nothing. That's the answer. You do realize how ..... life works, right? Did you find out that 1 + 1 = 2, then ask "what do you do with the 2?"
Square root of 3364 is 58. Because find the square of 4. Choose either 2 or 8. Cancel 2 digits. Square Root of 33 is Irriational Number. But remove the decimals. Then the answer is 58
Another quick way to find the correct answer between two choices is to cast out nines. For example, if the square root of 729 is either 23 or 27, we can first check 23 as a root by adding the digits together. 2+3 is 5, which gives us a remainder of 5. 23x23 gives us two remainders of 5, and we multiply them to get 25. 2+5=7. The nines remainder of 729 must also be 7, or we have the wrong root. 7+2+9=18, 1+8=9, and we can cast out the 9, giving us a remainder of zero. Seven does not equal zero, so 23 is not the correct root, and that leaves 27 as the only possible answer.
then the number isn't a perfect square, and the root isn't a neat rounded number (this method can't be used for numbers which aren't perfect squares to begin with)
1:41 so you saying 1525 1425 1325 1225 1125 1025 925 like you said answer would be 35 and how know square will be integer, bcoz non other those are LOL and that 5 meaningless but sure it wil bee 3 but that 5 fails. ou cant know did you make it correct. so how know?
58²=3,364
(a+b)²=a²+2ab+b²
(50+8)(50+8)
2,500+2(400)+64
2,500+800+64
3,300+64=3,364
(a-b)²=a²-2ab+b²
(60-2)(60-2)
3,600-2(120)+4
3,600-240+4
3,360+4=3,364
50^2 = 2500
8^2 = 64
25+8=33
3364
😅
Why 25+8??
@@dhruvsantra9027 because 58 is 8 away from 50. this trick revolves around 50. 42^2 for example would be 8 away from 50 and 8^2 is 64, 25-8 = 17 so 1764
Since this trick only applies to perfect squares, could you tell me how do I find out whether the number is a perfect square or not without the need to taking the square root of it, please?
Right now, I know one method for that called binomial expansion, but I’ll make a video if I find a simpler method.
Prime factorization.
If you can express the number as a product of prime factors in which there is exactly an even amount of each prime factor, or, in other words, when expressed in exponentiation form, all the exponents are even, then the number is a perfect square.
For example, the prime factorization of 900 is 2 x 2 x 3 x 3 x 5 x 5 or 2² x 3² x 5².
Since all the powers are even, then the number 900 is a perfect square. This is because 2² x 3² x 5² = (2 x 3 x 5)² = 30².
If you get the prime factorization of 500, that would be 2 x 2 x 5 x 5 x 5.
This is then written as 2² x 5³.
Since there is an odd number of 5s being multiplied, 500 isn't a perfect square.
Infact, if you take the square root of 2² x 5³, you are left with √(2² x 5³) =
√(2² x 5² x 5)
√2² x √5² x √5 =
2 x 5 x √5 =
10 x √5 =
10√5.
In short, find the prime factorization of the number. If you can group all the factors into pairs, without any left over, then the number is a square.
In fact, if you can group the prime factors of a number, in to groups of "n", then the number is a perfect nth power.
For example, if you take 1728, and find the prime factors, you will get 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3.
If we group these into pairs, we will get (2 x 2) x (2 x 2) x (2 x 2) x (3 x 3) x 3.
Since there is an extra '3' that isn't part of a pair, 1728 is _not_ a perfect square.
_However_ we can group these into 3s:
(2 x 2 x 2) x (2 x 2 x 2) x (3 x 3 x 3).
This means that 1728 is a perfect cube (power of 3).
In this case, if you take one number from each group, and multiply them, that is your cube root (i.e. 2 x 2 x 3 = 12).
You can just check your answer by squaring it
Ex: sqrt of 926
You just need to know some numbers like 10×10=100, 20×20=400, 30×30=900 and so on
You get the the number 30 forward and multiple then by thenselfs
30x30=900
31x31=961
So its about 30,5 or less,this part you calculate by hand to be easier
I hope yall get it,cuz it helps a lot 😅
Numbers ending in 2,3,7, or 8 are not perfect squares, Numbers ending with 0,1,4,5,6, or 9 can be, but are not necessarily.
It's a nice trick, but one small quibble. You started off saying you only need to learn the squares of 0 through 9, and you end by casually throwing in the square of 12.
Well finding the square of 12 is definetly better than finding the square root of 15876 (if it was possible without using this method) so i don't think its a big deal to complain about it
@@Bruh4502hi. Well, I wasn't actually complaining. I think it's a nice video, and I like nifty maths tricks like this.
You have to admit, though, that he did start off saying you only have to know squares up to 81, but within a few minutes he'd moved to, you all know the square of 12 is 144. My comment was really meant in a light-hearted way.
Sry...my bad
There is no way most people would be able to pick the number(s) who's square ends with the same digit as the square we're trying to find the root of, then remove the last two digits of the answer, then find the number who's square is less than the remaining part of the number without the last two digits, then multiply that number by the next number, then choose the greater of the two possible last digits, if the original number is greater than the number we got by multiplying the number who's square is less than the part of the number we got by removing the last two digits..... in 3 seconds.
Also, if the difficulty of a task is unrelated to the time it takes to do a task, then another way of finding the square root of a number, is the use of prime factorization.
For example, for 3364, we will find the prime factorization:
3364 | 2
1682 | 2
841 | 29
29 | 29
1
Now we simply write the product of the numbers in the second column, like so:
2 x 2 x 29 x 29
To simplify this, we can then rewrite this expression in the form of exponents:
2² x 29²
Then we can simply take the square root of this product, to find the answer is 2 x 29 = 58.
Way better trick but more complicated, I'm only In 6th grade and if i was in 8th grade I can do it, either way, thanks
@@yoro.jojjowi damn you better start studying now brother if you want iit
Hey thanks for this
But how we remove the square roots in the last step?
-does 58 have to get simplified
-does 58 have a square root?
-what do we do with 58 then?
@@Uninspiredz Um.... you are aware that 58 _IS_ the square root, right?
If you're asked to find the square root of 16, and you get 4, what do you do with the 4? Nothing. That's the answer. You do realize how ..... life works, right? Did you find out that 1 + 1 = 2, then ask "what do you do with the 2?"
@@scmtuk3662 bruh I forgot how it worked for a sec.
I just asked a Question, calm down
Sqrt[3364]=58
Please no spoilers
@@lukatolstov5598Then why are you reading the comment section before the video starts?
@@MarkGerald2011probably because it showed up when clicking on the video.
@@GomVorder78439 probably he's using his phone not pc or smth
@@lukatolstov5598it's not a spoiler because he doesn't solve this in the video
Tysm this helps me save so much time in solving problems
Square root of 3364 is 58. Because find the square of 4. Choose either 2 or 8. Cancel 2 digits. Square Root of 33 is Irriational Number. But remove the decimals. Then the answer is 58
@Brain Station how did you get 12 x 13 in 4:15
Multiply the number by the one after it
What is 12 + 1? 13 right? Here we are supposed to multiply the first number by it's successor, not the 2nd or 3rd number
@@tommytress77 why is Tommy here solving math problems 💀
@@Fire-b4 math good
🙂👍
misleading ... the trick allows you to quickly recognize a perfect square. it would take a normal person more like 30 seconds to apply the trick
Yep, I took 1 min to solve it
Can you make more videos that teaches tricks like this
this is helpful you are a good youtuber
Thanks.You made my life easier
Another quick way to find the correct answer between two choices is to cast out nines. For example, if the square root of 729 is either 23 or 27, we can first check 23 as a root by adding the digits together. 2+3 is 5, which gives us a remainder of 5. 23x23 gives us two remainders of 5, and we multiply them to get 25. 2+5=7. The nines remainder of 729 must also be 7, or we have the wrong root.
7+2+9=18, 1+8=9, and we can cast out the 9, giving us a remainder of zero. Seven does not equal zero, so 23 is not the correct root, and that leaves 27 as the only possible answer.
Amazing trick bro 🔥
What about numbers not having perfect square
this would 100% take longer than 3 seconds for starters
3364=4mod8
=(2mod8)x(2mod8)
33>5^2
64=8×8=4mod8
58=2mod8
can you give some extra problems after each vid?? it would help al lot
Sure
Broo got to chatgpt and say
Hey give me some 4 digit numbers of perfect square done
start with 60^2 = 3600 then minus 60, 59, 59 58 to get to 3364. So answer is 58
2:09 can we get 4^2 or 6^2 instead?
3:46 in this section why didn't you multiple 5×4
The rule is to multiply the number to its next number. n*(n+1)
whats the thing/rule that allows this trick to actually work?
How could crack like jee exams
If I only had 3 to 5 seconds i would have guessed wrong.. Might be easier to just "simply" _memorise_ them all..
ask a German if they know what the square root of 81 is, if they know, you get the correct answer, if they don’t know, you also get the correct answer
😂😂
Which app do you use to edit your videos?
So good, keep going 👏 💪
3364:- 2/8 and 5 then 58
How do we pick, choose the first number or the second number?
I'll just keep using the sqrt function on my calculator
appreciated 🔥
What If It ends in 2,3,7 or 8?
Just go for the closer one? Higher one or lower one?
then the number isn't a perfect square, and the root isn't a neat rounded number
(this method can't be used for numbers which aren't perfect squares to begin with)
@dinosatay thanks bro
Super thanks
Sqrt[9]
Also works for cuberoot
Bro what is the name of this trick😢
sqrt(3364) = 58.
does this work for all perfect squares?
That's because Jesse is at home, you're not. Time and feel again?
nice trick broo
and if the last number is 7 or 2?
Then it can't be a perfect square.
4:30 58
Fun fact
81x196=15876
1:41 so you saying 1525 1425 1325 1225 1125 1025 925 like you said answer would be 35 and how know square will be integer, bcoz non other those are LOL and that 5 meaningless but sure it wil bee 3 but that 5 fails. ou cant know did you make it correct. so how know?
I think this method only works for perfect squares
0:25 d4mass
58❤❤
Nice. But I'm afraid only useful in quizzes.
Trick without an explanation is just a trick
lol i calculated the first one in 5 seconds before watching the video
I may do this ib my calculator 😂
wait how did bro get 27 for the first one isn't it 35?
Root😊
I can just get a calculator and get the answer in less time than this video
waiting for you to get a calculator and press the button to get the answer? too slow,
two dights sq, must start with 5 and end with 8, END
didn't work for 998,001, at least not for me
With calculator its faster
58
Thumbs down for using a robot voice.
Skibidi
John 14:6
New King James Version
6 Jesus said to him, “I am the way, the truth, and the life. No one comes to the Father except through Me.
Noice
What a waste of time.....
Sqrt[729]=27
Sqrt[1225]=35
4:30 58
58
58
Sqrt[15876]=126
Sqrt[2916]=54
58
58
58