Algebra Examples

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

Step 1

Simplify the denominator.

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Step 1.1

Factor out $m^{2}$ .

$\frac{2 \sqrt{5 r}}{\sqrt{m^{2} m}}$

Step 1.2

Pull terms out from under the radical.

$\frac{2 \sqrt{5 r}}{| m | \sqrt{m}}$

Step 2

Multiply $\frac{2 \sqrt{5 r}}{| m | \sqrt{m}}$ by $\frac{\sqrt{m}}{\sqrt{m}}$ .

$\frac{2 \sqrt{5 r}}{| m | \sqrt{m}} \cdot \frac{\sqrt{m}}{\sqrt{m}}$

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply $\frac{2 \sqrt{5 r}}{| m | \sqrt{m}}$ by $\frac{\sqrt{m}}{\sqrt{m}}$ .

$\frac{2 \sqrt{5 r} \sqrt{m}}{| m | \sqrt{m} \sqrt{m}}$

Step 3.2

Move $\sqrt{m}$ .

$\frac{2 \sqrt{5 r} \sqrt{m}}{| m | (\sqrt{m} \sqrt{m})}$

Step 3.3

Raise $\sqrt{m}$ to the power of $1$ .

$\frac{2 \sqrt{5 r} \sqrt{m}}{| m | ({\sqrt{m}}^{1} \sqrt{m})}$

Step 3.4

Raise $\sqrt{m}$ to the power of $1$ .

$\frac{2 \sqrt{5 r} \sqrt{m}}{| m | ({\sqrt{m}}^{1} {\sqrt{m}}^{1})}$

Step 3.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2 \sqrt{5 r} \sqrt{m}}{| m | {\sqrt{m}}^{1 + 1}}$

Step 3.6

Add $1$ and $1$ .

$\frac{2 \sqrt{5 r} \sqrt{m}}{| m | {\sqrt{m}}^{2}}$

Step 3.7

Rewrite ${\sqrt{m}}^{2}$ as $m$ .

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Step 3.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{m}$ as $m^{\frac{1}{2}}$ .

$\frac{2 \sqrt{5 r} \sqrt{m}}{| m | {(m^{\frac{1}{2}})}^{2}}$

Step 3.7.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{2 \sqrt{5 r} \sqrt{m}}{| m | m^{\frac{1}{2} \cdot 2}}$

Step 3.7.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{2 \sqrt{5 r} \sqrt{m}}{| m | m^{\frac{2}{2}}}$

Step 3.7.4

Cancel the common factor of $2$ .

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Step 3.7.4.1

Cancel the common factor.

$\frac{2 \sqrt{5 r} \sqrt{m}}{| m | m^{\frac{2}{2}}}$

Step 3.7.4.2

Rewrite the expression.

$\frac{2 \sqrt{5 r} \sqrt{m}}{| m | m^{1}}$

Step 3.7.5

Simplify.

$\frac{2 \sqrt{5 r} \sqrt{m}}{| m | m}$

Step 4

Combine using the product rule for radicals.

$\frac{2 \sqrt{m \cdot 5 r}}{| m | m}$

Step 5

Move $5$ to the left of $m$ .

$\frac{2 \sqrt{5 \cdot m r}}{| m | m}$

Step 6

Reorder factors in $\frac{2 \sqrt{5 m r}}{| m | m}$ .

$\frac{2 \sqrt{5 m r}}{m | m |}$