Which of the following is equal to (2^3√3/√2)^3? : Problem Solving (PS)

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

13 Apr 2016, 04:45

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bgbeidas wrote:

Not sure I fully understood your explanation to the question, is Bunuel around at all?

since thesee are standard number properties, even Bunuel will have to explain exactly what has been written ..
But may be I'll write it in detail..
\((\frac{2*\sqrt[3]{3}}{\sqrt{2}})^3\)

Substitute the values as following as-
\(2= \sqrt{2}*\sqrt{2}\)...
\(and 3= \sqrt[3]{3}*\sqrt[3]{3}*\sqrt[3]{3}\)...
\(2\sqrt{2}= \sqrt{2}*\sqrt{2}*\sqrt{2}\)...

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

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

13 Apr 2016, 02:39

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bgbeidas wrote:

Apologies in advance for the poor formatting, it's my first time posting a question on here.

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

A) 3√2/2
B) 3√2
C) 6√2
D) 12
E) 12√2

If anyone looking to edit the question can't interpret the above please let me know.

Hi,

i believe the Q is meant to be..
\((\frac{2*\sqrt[3]{3}}{\sqrt{2}})^3\)
=>\((\sqrt{2}*\sqrt[3]{3})^3\)
=> \(2\sqrt{2}*3 = 6\sqrt{2}\)
C

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

03 Aug 2016, 09:53

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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

We can simplify the expression inside the parentheses first.

Recall that x/√x = √x, so 2/√2 = √2 and hence 2 x (^3√3)/√2 = √2 x (^3√3)

Now we raise each term to the 3rd power:

[√2 x (^3√3)]^3 = (√2)^3 x (^3√3)^3 = 2√2 x 3 = 6√2

(Note: When we raise each factor to the 3rd power, we use the fact that:

(√x)^3 = x√x and (^3√x)^3 = x) .

Answer: C

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

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

Answer: C

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

16 Jul 2016, 07:49

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Never mind. I thought the original question was 2^3 instead of 3 root of 3...

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

15 Aug 2016, 05:49

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AfricanPrincess wrote:

The way the question has been asked is ambiguous because of what looks like 2^3 in the numerator.

Posted from my mobile device

Totally agreed with you, I encountered this question today, and thought the number 3 in this case is the power of 2 and therefore can not arrived at the correct answer. I had to guess after 4m trying hopelessly to solve it, very frustrating as it is just the second question, I thought the answer is wrong. I think GMAT should make it clear which number belong to which.

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

16 Feb 2017, 12:16

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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

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

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

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

\(= \frac{12*√2}{2}\)

\(= 6√2\)

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]

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

13 Apr 2016, 23:47

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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

Thank you Abhishek, you made the math much more clear. However, I am still confused as to how the root 2 jumped to the top, and where the original 2 up top disappeared to.

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

14 Apr 2016, 02:49

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bgbeidas wrote:

Thank you Abhishek, you made the math much more clear. However, I am still confused as to how the root 2 jumped to the top, and where the original 2 up top disappeared to.

I think you are referring to the the following part as under -

Quote:

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

If that is the case then consider it this way -

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

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

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

=>\(\sqrt{2}\)

Hope this helps !! :-D

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

15 Apr 2016, 02:30

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bgbeidas wrote:

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

Thank you Abhishek, you made the math much more clear. However, I am still confused as to how the root 2 jumped to the top, and where the original 2 up top disappeared to.

ITS called " RATIONALISING THE DENOMINATOR"

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

11 Aug 2016, 15:55

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Why does the original equation have to be simplified?

Why can't tip 6 from "Exponents and roots: Tips and hints" post by bunuel be applied in this situation? (Can't post links yet)

I understand that you can't, because if you distribute the exponent and raise all the individual elements to 3 you get 8*3 / 2sqrt2 and ultimately 12/sqrt2.

What rule am I violating?

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

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]

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]

28 May 2018, 15:03

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ScottTargetTestPrep wrote:

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

Are we sure that it is indeed asking for 3rd root 3? I got this question today and it looks like 2^3 to me.. I took a screenshot to show the question.

I don't mean to bump an old topic but do I need to get my eyes checked?

Attachments

Screen Shot 2018-05-28 at 5.01.13 PM.png [ 19.36 KiB | Viewed 6234 times ]

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

13 Apr 2016, 04:33

Not sure I fully understood your explanation to the question, is Bunuel around at all?

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

13 Apr 2016, 07:28

chetan2u wrote:

bgbeidas wrote:

Not sure I fully understood your explanation to the question, is Bunuel around at all?

since thesee are standard number properties, even Bunuel will have to explain exactly what has been written ..
But may be I'll write it in detail..
\((\frac{2*\sqrt[3]{3}}{\sqrt{2}})^3\)

Substitute the values as following as-
\(2= \sqrt{2}*\sqrt{2}\)...
\(and 3= \sqrt[3]{3}*\sqrt[3]{3}*\sqrt[3]{3}\)...
\(2\sqrt{2}= \sqrt{2}*\sqrt{2}*\sqrt{2}\)...

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

gmatclubot

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

13 Apr 2016, 07:28

GMAT Problem Solving (PS) Questions

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