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(√x)x can be expressed as:

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(√x)x can be expressed as: [#permalink]

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New post 10 Apr 2018, 00:08
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

66% (00:24) correct 34% (00:34) wrong based on 123 sessions

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(√x)x can be expressed as: [#permalink]

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New post 10 Apr 2018, 00:18
Bunuel wrote:
\((\sqrt{x})x\) can be expressed as:


A. \(\sqrt{x^2}\)

B. \(x^3\)

C. \(\sqrt{x^3}\)

D. \(\frac{x^2}{2}\)

E. \(\sqrt[3]{x^2}\)


Formula used: \(a^m * a^n = a^{m+n}\)


The expression can be simplified as follows: \((\sqrt{x})x = (x^{\frac{1}{2}})x^1 = x^{\frac{1}{2} + 1} = x^{\frac{3}{2}} = \sqrt{x^3}\)

Therefore, \((\sqrt{x})x\) can be expressed as \(\sqrt{x^3}\)(Option C)
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Re: (√x)x can be expressed as: [#permalink]

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New post 10 Apr 2018, 00:19
Bunuel wrote:
\((\sqrt{x})x\) can be expressed as:


A. \(\sqrt{x^2}\)

B. \(x^3\)

C. \(\sqrt{x^3}\)

D. \(\frac{x^2}{2}\)

E. \(\sqrt[3]{x^2}\)


As all we're given is equations, we'll use a simplification based approach.
This is a Precise methodology.

\(\sqrt{x}=x^\frac{1}{2}\)
\(x^\frac{1}{2}*x=x^{\frac{1}{2}+1}=x^\frac{3}{2}=\sqrt{x^3}\)

(C) is our answer.
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Re: (√x)x can be expressed as: [#permalink]

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New post 10 Apr 2018, 00:57

Solution



Given:
    • We are given an expression (\(\sqrt{x}\))x.

To find:
    • We need to find the simplified form of (\(\sqrt{x}\))x.

Approach and Working:

    By the application of \(a^m * a^n = a^{(m+n)}\), we can write\(\sqrt{x}\)= \(x^{1/2}\)
    • Thus, (\(\sqrt{x}\)) \(x\)= \(x^{\frac{1}{2}}\)* \(x\)
    • =\(x ^{(1+\frac{1}{2})}\)
    • = \(x^\frac{3}{2}\)= By applying \((a^m)^{n}\)= \(a^{mn}\), we can write \(x^{\frac{3}{2}}\) as \((x^3)^{\frac{1}{2}}\)
    • = \(\sqrt{(x^3)}\)

Thus, \((\sqrt{x})x\) can be expressed as \(\sqrt{(x^3)}\)


Hence, the correct answer is option C.

Answer: C
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(√x)x can be expressed as: [#permalink]

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New post 11 Apr 2018, 06:39
Bunuel wrote:
\((\sqrt{x})x\) can be expressed as:


A. \(\sqrt{x^2}\)

B. \(x^3\)

C. \(\sqrt{x^3}\)

D. \(\frac{x^2}{2}\)

E. \(\sqrt[3]{x^2}\)


\(x = \sqrt{x^2}\)

Therefore:

\((\sqrt{x})x\) = \((\sqrt{x})\sqrt{x^2}\) = \(\sqrt{x^3}\)

Answer: C

Another appraoch:

Let x = 2

Substitute in each answer choice

c = \(\sqrt{2^3}\) = \((\sqrt{2})2\)
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Re: (√x)x can be expressed as: [#permalink]

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New post 11 Apr 2018, 09:56
Bunuel wrote:
\((\sqrt{x})x\) can be expressed as:


A. \(\sqrt{x^2}\)

B. \(x^3\)

C. \(\sqrt{x^3}\)

D. \(\frac{x^2}{2}\)

E. \(\sqrt[3]{x^2}\)


\(\sqrt{x}\)\(*x\)

\(x^\frac{1}{2}*{x^1}\)

\({x^\frac{3}{2}}\)

\(\sqrt{x^3}\)

Hence (C)
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Re: (√x)x can be expressed as: [#permalink]

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New post 12 Apr 2018, 15:58
Bunuel wrote:
\((\sqrt{x})x\) can be expressed as:


A. \(\sqrt{x^2}\)

B. \(x^3\)

C. \(\sqrt{x^3}\)

D. \(\frac{x^2}{2}\)

E. \(\sqrt[3]{x^2}\)


We can re-express the expression as:

x^(1/2) * x^1 = x^(1/2 + 1) = x^(3/2) = √(x^3)

Answer: C
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Re: (√x)x can be expressed as:   [#permalink] 12 Apr 2018, 15:58
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