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Which of the following is equal to (2^3√3/√2)^3?

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Re: Which of the following is equal to (2^3√3/√2)^3? [#permalink]

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New post 09 Sep 2016, 06:31
i stopped for a second to check whether 12/sqrt(2) is the answer..but it was not..so I multiplied everything by sqrt(2)/sqrt(2) so that to eliminate the fraction (basically multiplying by 1!) and got 6*sqrt(2)

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Re: Which of the following is equal to (2^3√3/√2)^3? [#permalink]

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New post 29 Jan 2017, 12:46
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crowle35 wrote:
IMO - the wording on this problem is ambiguous. How am I supposed to know it is 2(CUBERT(3)) instead of 2^3(Sqrt(3))???



I agree but 2^3 version does not have a solution below. I wasted time thinking that it was 2^3 just to realize that was not the actual question. Pretty poor question if you ask me.
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Re: Which of the following is equal to (2^3√3/√2)^3? [#permalink]

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New post 29 Jan 2017, 12:52
Wofford09 wrote:
crowle35 wrote:
IMO - the wording on this problem is ambiguous. How am I supposed to know it is 2(CUBERT(3)) instead of 2^3(Sqrt(3))???



I agree but 2^3 version does not have a solution below. I wasted time thinking that it was 2^3 just to realize that was not the actual question. Pretty poor question if you ask me.


As far as the questions goes

2^3/ 2^(3/2) = 2^(6/2)/ 2^(3/2) and for exponents you subtract so 6/2 - 3/2 = 3/2 or 2^(3/2) which equals 2\sqrt{2}. Multiply that by 3 (for the 3 cubed root 3 piece) and you arrive at answer C
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Re: Which of the following is equal to (2^3√3/√2)^3? [#permalink]

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New post 14 Feb 2017, 05:38
crowle35 wrote:
IMO - the wording on this problem is ambiguous. How am I supposed to know it is 2(CUBERT(3)) instead of 2^3(Sqrt(3))???


I got into the same dilemma in my mock and ultimately guessed wrongly.
I also thought in the numerator it is (2 raised to the power 3), whereas it is (2 * cube-root of 3)

I guess a better way to approach this problem or any such ambiguous problem on the exam would be to change the approach of reading the question once I find out that my calculation is not matching any of the answer choices. After spending 1 min. on the problem, if I am not getting anywhere around, I must change my way of reading the question OR the way of solving. This is a lesson for me.

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Re: Which of the following is equal to (2^3√3/√2)^3? [#permalink]

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bgbeidas wrote:
Which of the following is equal to \((\frac{2*\sqrt[3]{3}}{\sqrt{2}})^3\)?

A) 3√2/2
B) 3√2
C) 6√2
D) 12
E) 12√2


Let’s simplify the expression [(2 * ^3√3)/√2]^3.

Distributing the exponent of 3, we have:

(2^3)(^3√3)^3/(√2)^3

(8 x 3)/(2√2) = 12/√2

We must rationalize the denominator. Multiplying 12/√2 by √2/√2, we have:

12√2/2 = 6√2

Answer: C
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Re: Which of the following is equal to (2^3√3/√2)^3? [#permalink]

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New post 16 Feb 2017, 11:16
bgbeidas wrote:
Which of the following is equal to \((\frac{2*\sqrt[3]{3}}{\sqrt{2}})^3\)?

A) 3√2/2
B) 3√2
C) 6√2
D) 12
E) 12√2


\(= \frac{2^3*3}{2\sqrt{2}}\)

\(= \frac{8*3}{2\sqrt{2}}\)

\(= \frac{12}{\sqrt{2}}\)

\(= \frac{12*√2}{2}\)

\(= 6√2\)

Thus, answer will be (C) \(6√2\)
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Re: Which of the following is equal to (2^3√3/√2)^3? [#permalink]

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New post 14 Jun 2017, 05:58
Abhishek009 wrote:
bgbeidas wrote:

=>\((\sqrt{2}*\sqrt[3]{3})^3\)
=> \(2\sqrt{2}*3 = 6\sqrt{2}\)
C

I understand how you got 3, and how you should gt 2\sqrt{2} at the bottom.
But the 2 in the top part, when I cube it I get 8, not sure where that disappears in your process.



I think u are clear with this part =>\((\sqrt{2}*\sqrt[3]{3})^3\)

=>\((\sqrt{2}*\sqrt[3]{3})^3\)

=> (\(2^{1/2}\) * \(3^{1/3}\))\(^{3}\)

=> \(2^{3/2}\)* \(3^{3/3}\)

=>\(2^1\)* \(2^{1/2}\)* \(3^1\) { Because \(\frac{3}{2}\) = \(1 \frac{1}{2}\) and \(\frac{3}{3}\) = 1 }

=> \(2^1\)* \(2^{1/2}\)* \(3^1\)

=> 2*\(\sqrt{2}\) * 3

=>6\(\sqrt{2}\)


Hope this helps !!
:-D :-D


Thx for this perfect explanation :-D

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Re: Which of the following is equal to (2^3√3/√2)^3? [#permalink]

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New post 29 Jul 2017, 10:31
As with some others, I faced difficulty in recognizing the question because of the poor presentation by Gmat prep. I am quite annoyed and hope I dont encounter a question with such a horrid presentation in the actual exam.

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Re: Which of the following is equal to (2^3√3/√2)^3? [#permalink]

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New post 06 Sep 2017, 02:08
crowle35 wrote:
IMO - the wording on this problem is ambiguous. How am I supposed to know it is 2(CUBERT(3)) instead of 2^3(Sqrt(3))???



THis same thing happened to me while I was taking my GMAT prep. The text seemed very ambiguous.

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Re: Which of the following is equal to (2^3√3/√2)^3? [#permalink]

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New post 30 Sep 2017, 07:00
bgbeidas wrote:
Which of the following is equal to \((\frac{2*\sqrt[3]{3}}{\sqrt{2}})^3\)?

A) 3√2/2
B) 3√2
C) 6√2
D) 12
E) 12√2


if the exponents are distributed, we get

(2^3 x 3)/ 2 x √2

= 24/ 2 x √2
= 12/ √2

now, so far I know, there is an unofficial rule in math that states that radical such as "√" cannot be in the denominator
so we have to rationalize it..
= (12 x √2)/ 2
= 6 x √2 (answer)

cheers through the kudos button if this helps
thanks 8-)

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Re: Which of the following is equal to (2^3√3/√2)^3?   [#permalink] 30 Sep 2017, 07:00

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