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# Which of the following equals x^(1/2)*x^(1/3)

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Math Expert
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Which of the following equals x^(1/2)*x^(1/3)  [#permalink]

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26 Aug 2018, 20:13
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25% (medium)

Question Stats:

61% (00:34) correct 39% (00:42) wrong based on 109 sessions

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Which of the following equals $$(\sqrt[2]{x})(\sqrt[3]{x})$$?

(A) $$\sqrt[5]{x}$$

(B) $$\sqrt[6]{x}$$

(C) $$\sqrt[3]{x^2}$$

(D) $$\sqrt[5]{x^6}$$

(E) $$\sqrt[6]{x^5}$$

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Which of the following equals x^(1/2)*x^(1/3)  [#permalink]

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26 Aug 2018, 20:23
1
Bunuel wrote:
Which of the following equals $$(\sqrt[2]{x})(\sqrt[3]{x})$$?

(A) $$\sqrt[5]{x}$$

(B) $$\sqrt[6]{x}$$

(C) $$\sqrt[3]{x^2}$$

(D) $$\sqrt[5]{x^6}$$

(E) $$\sqrt[6]{x^5}$$

$$(\sqrt[2]{x})(\sqrt[3]{x})$$ can be written as:

$$x^{\frac{1}{2}}*x^{\frac{1}{3}}$$
$$=x^{\frac{1}{2}+\frac{1}{3}}$$
$$=x^{\frac{5}{6}}$$
$$=(x^5)^{\frac{1}{6}}$$
$$=\sqrt[6]{x^5}$$

Ans. (E)
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Which of the following equals x^(1/2)*x^(1/3)  [#permalink]

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27 Aug 2018, 06:47
1
Bunuel wrote:
Which of the following equals $$(\sqrt[2]{x})(\sqrt[3]{x})$$?

(A) $$\sqrt[5]{x}$$

(B) $$\sqrt[6]{x}$$

(C) $$\sqrt[3]{x^2}$$

(D) $$\sqrt[5]{x^6}$$

(E) $$\sqrt[6]{x^5}$$

$$(\sqrt[2]{x})(\sqrt[3]{x})$$

= $$x^{\frac{1}{2} + \frac{1}{3}}$$

= $$x^{\frac{3+2}{6}}$$

= $$x^{\frac{5}{6}}$$, Answer must be (E)
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Re: Which of the following equals x^(1/2)*x^(1/3)  [#permalink]

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27 Aug 2018, 07:01
1
Abhishek009 wrote:
Bunuel wrote:
Which of the following equals $$(\sqrt[2]{x})(\sqrt[3]{x})$$?

(A) $$\sqrt[5]{x}$$

(B) $$\sqrt[6]{x}$$

(C) $$\sqrt[3]{x^2}$$

(D) $$\sqrt[5]{x^6}$$

(E) $$\sqrt[6]{x^5}$$

$$(\sqrt[2]{x})(\sqrt[3]{x})$$

= $$x^{\frac{1}{2} + \frac{1}{3}}$$

= $$x^{\frac{3+2}{6}}$$

= $$x^{\frac{5}{6}}$$, Answer must be (D)

Hi Abhishek009,
Final simplified expression corresponds to option (E).

Posted from my mobile device
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Regards,

PKN

Rise above the storm, you will find the sunshine

Math Expert
Joined: 02 Aug 2009
Posts: 7205
Re: Which of the following equals x^(1/2)*x^(1/3)  [#permalink]

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27 Aug 2018, 07:39
Bunuel wrote:
Which of the following equals $$(\sqrt[2]{x})(\sqrt[3]{x})$$?

(A) $$\sqrt[5]{x}$$

(B) $$\sqrt[6]{x}$$

(C) $$\sqrt[3]{x^2}$$

(D) $$\sqrt[5]{x^6}$$

(E) $$\sqrt[6]{x^5}$$

$$(\sqrt[2]{x})(\sqrt[3]{x})$$=$$x^{\frac{1}{2}}*x^{\frac{1}{3}}=x^{\frac{1}{2}+\frac{1}{3}}=x^{\frac{5}{6}}$$=$$\sqrt[6]{x^5}$$

E

Another way..

Take some smart value of x, that is x should be both square and cube
Let's take some square of a prime number so pick up 4..
So x^3=4^3=64
$$(\sqrt[2]{x})(\sqrt[3]{x})$$= $$(\sqrt[2]{64})(\sqrt[3]{64})$$=8*4=32

Let's see the choice

(E) $$\sqrt[6]{x^5}=\sqrt[6]{64^5}=\sqrt[6]{(2^6)^5}=\sqrt[6]{2^{30}}=2^5=32$$
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: Which of the following equals x^(1/2)*x^(1/3)  [#permalink]

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27 Aug 2018, 10:29
PKN wrote:
Final simplified expression corresponds to option (E).

Posted from my mobile device

Edited thanks for pointing out...
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Thanks and Regards

Abhishek....

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Re: Which of the following equals x^(1/2)*x^(1/3) &nbs [#permalink] 27 Aug 2018, 10:29
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