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# (√x)x can be expressed as:

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Math Expert
Joined: 02 Sep 2009
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(√x)x can be expressed as:  [#permalink]

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10 Apr 2018, 00:08
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25% (medium)

Question Stats:

65% (00:24) correct 35% (00:36) wrong based on 130 sessions

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$$(\sqrt{x})x$$ can be expressed as:

A. $$\sqrt{x^2}$$

B. $$x^3$$

C. $$\sqrt{x^3}$$

D. $$\frac{x^2}{2}$$

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

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

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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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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.

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

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

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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.

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

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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:

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

Another appraoch:

Let x = 2

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

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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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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)

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