Square root of (4/7 * 14/3) =? How WELL do you UNDERSTAND Square Roots?
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- Опубліковано 2 жов 2024
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Very long-winded explanation! 1 1/2 minutes would have been plenty.
If only we were all as advanced as you
Personally, I would finish it up with √24 / 3.
Cancel 7 with 14 leads to sqrt(4*2/3) or 2*sqrt(2/3). This cannot stay like this. Multiply with sqrt(3)/sqrt(3), which leads to (2*sqrt(2*3))/3 or 2*sqrt(6)/3 or answer b)!
Best way to answer and i spent less than 1 minute the figure it out.
Of course 2√(2/3) can stay like that. That's what you'd get to if all you were doing was simplifying the expression.
But obviously we have to go further here because 2√(2/3) is not one of the multiple choice options.
The answer is b
Learn why: 7 in the denominator of the first fraction in the square root cancels out with 14 in the numerator of the second fraction in the square root, resulting in √2/3
Then, in order to simplify the expression as much as possible, we take √4 apart and write it as 2 • √2/3
So, now that we know √a/b = √a/√b
Thus: 2 • √2/3 = 2√2/√3
Now we just have to make the denominator rational, by multiplying it by √3 in both nominator and denominator, simply a 1 which is √3/√3
As we do so, we reach the answer of: 2√6/3
B
Simply multiply, and then simplify.
I think that removing the sevens in the numerator AND denominator is the "first step" that should be taken before considering the radicalized nature of the expression. Then you immediately get sqrt(8/3) and it's already time to get the calculator out. Even after the three extra steps to "prettify" the expression you still need to whip the calculator out anyhow. I'm also dubious about the "sinfulness" of a radical in the denominator.
Seems better just to leave the denominator as is. Rationalizing could easily lead to errors.
You mean leave the square root of 3 in the denominator? If so then that is the wrong answer
This guy has a bit of a weird obsession about rationalising denominators.
2√(2/3) or (2√2)/√3 are obviously fine, but neither of them are in the multiple choice options, so we need to go further to find the correct answer here.
@@bigdog3628I think what they're suggesting is that the question could have given 2√(2/3) or (2√2)/√3 as an option, since that's where you'd get to if you were simplifying the original expression.
2*sqrt(2/3) -> is equal with b.
√(4x14 divided by 7 x 3) cross the 7s and √(4 x 2 divided by 3) and that becomes 2√(2 /3). Reduce the sqrt by multiplying the 2 and the 3 by 3 each and results 2√(6 / 9) take √9 and the results is (2/3)√6.
Yup, I'm relearning. Thank you, UA-cam man.😊
Ben, je l'ai fait de tête, en 5 secondes !
I got b) as math instructors don't like to leave an irrational number in the denominator, so the final result has us multiplying by 1 in the form of sqrt(3)/sqrt(3) to give 3 in the denominator, and sqrt(6) in the numerator.
Split the 14 in to 2 × 7. The 7's can cancel each other out. Now you have sqrt(4(2/3)) bring out the 4 to get 2(sqrt(2/3)). You can also get the same answer by splitting up everything in primes and use substitution. a = 2, b = 3, c = 7. Sqrt((a²×a×c)/(b×c)). The c cancels out, and the a² moves out of the square root. You are left with a(sqrt(a/b)) = 2(sqrt(2/3)). If you don't like the square root in the denominator, then it is 2((sqrt(6))/3).
Mr ecro. Your answer is perfectly correct. No need to rationalize denominator
Why is the answer always b)?
😂
This identical problem was presented twice before, 2 months ago, and 4 months ago. Apparently, many got this wrong because the previous ones were NOT multiple choice.
RQ (4/7) / (14/3) = ?
Simplificando o 14 em 14/7 com o 7 em 4/7, vem (RQ 4) / (2/3 ) =
(RQ 8) / (RQ 3 =
2 RQ 2 / RQ 3 =
4 / RQ 3 , opção a)
Working it out on paper, I got b.
b)
I only used geometry in my lifetime
4 / raiz cuadrada de 3 el resultado.
At 12:10 you say, regarding the denominator (SQRT(3)) that "...we have a square root of an irrational number in the denominator...". Did you men "we have an irrational denominator", (SQRT(3))? It is repeated at 13:50
b) 2√6/3
I took another path which is legit as well.
2/SQ 7 X SQ 2 X SQ 7/SQ 3. I cross cancelled both SQ 7 and it left me with 2(SQ 2)/SQ 3.
Then I rationalized the denominator and got the right answer.
b
B
B
b).
b) 2√6/3
ตอบข้อ B ครับ
ME EQUIVOQUE 2 RAIZ CUADRADA DE 2 / 3 LA CORRECTA .
2 racine de 6/ 3
Don’t know what you don’t know
great reduction thanks for the lesson
b) 2sq.root of 6/3
B
Its not a problem at all.
b)
I get 2*(sqrt 2/3). This is the same as answer (b) but why do you write it the way you do?
Because you should rationalize the denominator („no roots in the lower part of a fraction“!)
@@philipkudrna5643
There's no reason in general why you should rationalise the denominator. (2√6)/3 and 2√(2/3) are just different ways of writing the same thing.
But of course, when a question says "which of these for options is equivalent to the original expression?", and (2√6)/3 is one of the options but 2√(2/3) is not one of the options, then 2√(2/3) is obviously not the correct answer to that specific question.