Pre-Algebra Examples

$\frac{\sqrt{120 x^{7}}}{\sqrt{30 x^{2}}}$

Step 1

Combine $\sqrt{120 x^{7}}$ and $\sqrt{30 x^{2}}$ into a single radical.

$\sqrt{\frac{120 x^{7}}{30 x^{2}}}$

Step 2

Reduce the expression $\frac{120 x^{7}}{30 x^{2}}$ by cancelling the common factors.

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Step 2.1

Factor $30$ out of $120 x^{7}$ .

$\sqrt{\frac{30 (4 x^{7})}{30 x^{2}}}$

Step 2.2

Factor $30$ out of $30 x^{2}$ .

$\sqrt{\frac{30 (4 x^{7})}{30 (x^{2})}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{30 (4 x^{7})}{30 x^{2}}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{4 x^{7}}{x^{2}}}$

Step 3

Cancel the common factor of $x^{7}$ and $x^{2}$ .

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Step 3.1

Factor $x^{2}$ out of $4 x^{7}$ .

$\sqrt{\frac{x^{2} (4 x^{5})}{x^{2}}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\sqrt{\frac{x^{2} (4 x^{5})}{x^{2} \cdot 1}}$

Step 3.2.2

Cancel the common factor.

$\sqrt{\frac{x^{2} (4 x^{5})}{x^{2} \cdot 1}}$

Step 3.2.3

Rewrite the expression.

$\sqrt{\frac{4 x^{5}}{1}}$

Step 3.2.4

Divide $4 x^{5}$ by $1$ .

$\sqrt{4 x^{5}}$

Step 4

Rewrite $4 x^{5}$ as ${(2 x^{2})}^{2} x$ .

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Step 4.1

Rewrite $4$ as $2^{2}$ .

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

Step 4.2

Factor out $x^{4}$ .

$\sqrt{2^{2} (x^{4} x)}$

Step 4.3

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

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

Step 4.4

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

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

Step 5

Pull terms out from under the radical.

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