Pre-Algebra Examples

$\frac{\sqrt{250 x^{16}}}{\sqrt{2 x}}$

Step 1

Combine $\sqrt{250 x^{16}}$ and $\sqrt{2 x}$ into a single radical.

$\sqrt{\frac{250 x^{16}}{2 x}}$

Step 2

Reduce the expression $\frac{250 x^{16}}{2 x}$ by cancelling the common factors.

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Step 2.1

Factor $2$ out of $250 x^{16}$ .

$\sqrt{\frac{2 (125 x^{16})}{2 x}}$

Step 2.2

Factor $2$ out of $2 x$ .

$\sqrt{\frac{2 (125 x^{16})}{2 (x)}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{2 (125 x^{16})}{2 x}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{125 x^{16}}{x}}$

Step 3

Cancel the common factor of $x^{16}$ and $x$ .

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Step 3.1

Factor $x$ out of $125 x^{16}$ .

$\sqrt{\frac{x (125 x^{15})}{x}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Raise $x$ to the power of $1$ .

$\sqrt{\frac{x (125 x^{15})}{x^{1}}}$

Step 3.2.2

Factor $x$ out of $x^{1}$ .

$\sqrt{\frac{x (125 x^{15})}{x \cdot 1}}$

Step 3.2.3

Cancel the common factor.

$\sqrt{\frac{x (125 x^{15})}{x \cdot 1}}$

Step 3.2.4

Rewrite the expression.

$\sqrt{\frac{125 x^{15}}{1}}$

Step 3.2.5

Divide $125 x^{15}$ by $1$ .

$\sqrt{125 x^{15}}$

Step 4

Rewrite $125 x^{15}$ as ${(5 x^{7})}^{2} \cdot (5 x)$ .

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Step 4.1

Factor $25$ out of $125$ .

$\sqrt{25 (5) x^{15}}$

Step 4.2

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 5 x^{15}}$

Step 4.3

Factor out $x^{14}$ .

$\sqrt{5^{2} \cdot 5 (x^{14} x)}$

Step 4.4

Rewrite $x^{14}$ as ${(x^{7})}^{2}$ .

$\sqrt{5^{2} \cdot 5 ({(x^{7})}^{2} x)}$

Step 4.5

Move $5$ .

$\sqrt{5^{2} {(x^{7})}^{2} \cdot 5 x}$

Step 4.6

Rewrite $5^{2} {(x^{7})}^{2}$ as ${(5 x^{7})}^{2}$ .

$\sqrt{{(5 x^{7})}^{2} \cdot 5 x}$

Step 4.7

Add parentheses.

$\sqrt{{(5 x^{7})}^{2} \cdot (5 x)}$

Step 5

Pull terms out from under the radical.

$5 x^{7} \sqrt{5 x}$