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

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

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New post 26 Aug 2018, 21:13
1
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A
B
C
D
E

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  25% (medium)

Question Stats:

65% (00:37) correct 35% (00:48) wrong based on 128 sessions

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

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New post 26 Aug 2018, 21:23
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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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New post 27 Aug 2018, 07:47
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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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New post 27 Aug 2018, 08:01
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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Re: Which of the following equals x^(1/2)*x^(1/3)  [#permalink]

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New post 27 Aug 2018, 08:39
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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Re: Which of the following equals x^(1/2)*x^(1/3)  [#permalink]

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New post 27 Aug 2018, 11:29
PKN wrote:
Final simplified expression corresponds to option (E).

Posted from my mobile device

Edited thanks for pointing out... :sad:
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Re: Which of the following equals x^(1/2)*x^(1/3)   [#permalink] 27 Aug 2018, 11:29
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