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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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09 Sep 2016, 07:31
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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29 Jan 2017, 13:46
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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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29 Jan 2017, 13:52
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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14 Feb 2017, 06:38
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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15 Feb 2017, 16:13
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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

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

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16 Feb 2017, 12:16
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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14 Jun 2017, 06:58
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 !!

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

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29 Jul 2017, 11:31
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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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06 Sep 2017, 03:08
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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))???

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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30 Sep 2017, 08:00
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

cheers through the kudos button if this helps
thanks
Re: Which of the following is equal to (2^3√3/√2)^3?   [#permalink] 30 Sep 2017, 08:00

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