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If @(n) is defined as the product of the cube root of n and the positive square root of n, then for what number n does @(n)=50 percent of n?

A. 16 B. 64 C. 100 D. 144 E. 729

Given: \(@(n)=\sqrt[3]{n}*\sqrt[2]{n}\). Question: if \(@(n)=0.5n\) then \(n=?\)

So we have that \(\sqrt[3]{n}*\sqrt[2]{n}=\frac{1}{2}*n\) --> \(2*\sqrt[3]{n}*\sqrt[2]{n}=n\) --> take to the 6th power --> \(64*n^2*n^3=n^6\) --> \(n=64\).

Just follow the rules of exponents. Answer will follow. Cube root is the power of 1/3. Square root is the power of 1/2

\(n^{\frac{1}{3}}*n^{\frac{1}{2}} = \frac{n}{2}\) You need to find n. So bring all n's together on one side of the equation and everything else on the other side.

the cube root of what integer power of 2 is closest to 50?

1)16 2) 17 3)18 4 ) 19 5) 20

can u pls help me in this by a quicker solution???????

Look at the powers of 2.

2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32 2^6 = 64 2^7 = 128 Since it is an exponential increase, the result increases much more as you go to higher and higher powers. Which powers of 2 are around 50? 2^5 = 32 2^6 = 64 50 is almost in the middle of the two of them but closer to 64. Also, the result increases more with higher powers so I would expect 50 to be almost 2^(5.6) or a little higher.

If you find the cube root of 2^18, you will get (2^18)^(1/3) = 2^6 If you find the cube root of 2^17, you will get (2^17)^(1/3) = 2^(5.667) This is the closest. Answer is 17.
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19 Jul 2014, 09:36

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Re: If (n) is defined as the product of the cube root of n and [#permalink]

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10 Mar 2015, 03:31

VeritasPrepKarishma wrote:

GMATD11 wrote:

From B and E whts wrong with E

Just follow the rules of exponents. Answer will follow. Cube root is the power of 1/3. Square root is the power of 1/2

\(n^{\frac{1}{3}}*n^{\frac{1}{2}} = \frac{n}{2}\) You need to find n. So bring all n's together on one side of the equation and everything else on the other side.

Just follow the rules of exponents. Answer will follow. Cube root is the power of 1/3. Square root is the power of 1/2

\(n^{\frac{1}{3}}*n^{\frac{1}{2}} = \frac{n}{2}\) You need to find n. So bring all n's together on one side of the equation and everything else on the other side.

Re: If @(n) is defined as the product of the cube root of n and [#permalink]

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10 May 2016, 01:01

Hello from the GMAT Club BumpBot!

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Re: If @(n) is defined as the product of the cube root of n and [#permalink]

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26 Jun 2017, 07:01

Hello from the GMAT Club BumpBot!

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