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Ksenya-84 [330]

2 years ago

12

A rectangular prism has a length of 17 inches, a height of 15 inches, and a width of 17 inches. What is its volume, in cubic inc

hes?

1 answer:

frez [133]2 years ago

5 0

The volume of a rectangle prism is V=whl where w is the width, h is the height, and l is the length. In this case, V=17*15*17, or 4335 cubic inches.

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Which is equivalent to V180x11 after it has been simplified completely?

inna [77]

Question:

Which is equivalent to $\sqrt{180x^{11}}$ after it has been simplified completely?

Answer:

$\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}$

Step-by-step explanation:

Given

$\sqrt{180x^{11}}$

Required

Simplify

We start by splitting the square root

$\sqrt{180x^{11}} = \sqrt{180} * \sqrt{x^{11}}$

Replace 180 with 36 * 5

$\sqrt{180x^{11}} = \sqrt{36 * 5} * \sqrt{x^{11}}$

Further split the square roots

$\sqrt{180x^{11}} = \sqrt{36} *\sqrt{5} * \sqrt{x^{11}}$

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{11}}$

Replace power of x; 11 with 10 + 1

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10 + 1}}$

From laws of indices; $a^{m+n} = a^m * a^n$

So, we have

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10} * x^1}$

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10} * x}$

Further split the square roots

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10}} * \sqrt{x}$

From laws of indices; $\sqrt{a} = a^{\frac{1}{2}}$

So, we have

$\sqrt{180x^{11}} = 6*\sqrt{5} * x^{10*\frac{1}{2}} * \sqrt{x}$

$\sqrt{180x^{11}} = 6*\sqrt{5} * x^{\frac{10}{2}} * \sqrt{x}$

$\sqrt{180x^{11}} = 6*\sqrt{5} * x^{5} * \sqrt{x}$

Rearrange Expression

$\sqrt{180x^{11}} = 6 * x^{5} * \sqrt{5} * \sqrt{x}$

$\sqrt{180x^{11}} = 6x^{5} * \sqrt{5} * \sqrt{x}$

From laws of indices; $\sqrt{a} *\sqrt{b} = \sqrt{a*b} = \sqrt{ab}$

So, we have

$\sqrt{180x^{11}} = 6x^{5} * \sqrt{5*x}$

$\sqrt{180x^{11}} = 6x^{5} * \sqrt{5x}$

$\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}$

<em>The expression can no longer be simplified</em>

Hence, $\sqrt{180x^{11}}$ is equivalent to $6x^{5}\sqrt{5x}$

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