Pre-Algebra Examples

$\frac{\sqrt{45 m^{5}}}{\sqrt{5}}$

Step 1

Combine $\sqrt{45 m^{5}}$ and $\sqrt{5}$ into a single radical.

$\sqrt{\frac{45 m^{5}}{5}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Reduce the expression $\frac{45 m^{5}}{5}$ by cancelling the common factors.

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Step 2.1.1

Factor $5$ out of $45 m^{5}$ .

$\sqrt{\frac{5 (9 m^{5})}{5}}$

Step 2.1.2

Factor $5$ out of $5$ .

$\sqrt{\frac{5 (9 m^{5})}{5 (1)}}$

Step 2.1.3

Cancel the common factor.

$\sqrt{\frac{5 (9 m^{5})}{5 \cdot 1}}$

Step 2.1.4

Rewrite the expression.

$\sqrt{\frac{9 m^{5}}{1}}$

Step 2.2

Divide $9 m^{5}$ by $1$ .

$\sqrt{9 m^{5}}$

Step 3

Rewrite $9 m^{5}$ as ${(3 m^{2})}^{2} m$ .

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Step 3.1

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} m^{5}}$

Step 3.2

Factor out $m^{4}$ .

$\sqrt{3^{2} (m^{4} m)}$

Step 3.3

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

$\sqrt{3^{2} ({(m^{2})}^{2} m)}$

Step 3.4

Rewrite $3^{2} {(m^{2})}^{2}$ as ${(3 m^{2})}^{2}$ .

$\sqrt{{(3 m^{2})}^{2} m}$

Step 4

Pull terms out from under the radical.

$3 m^{2} \sqrt{m}$