Algebra Examples

$\frac{3 \sqrt{3}}{\sqrt{6 m}}$

Step 1

Combine $\sqrt{3}$ and $\sqrt{6 m}$ into a single radical.

$3 \sqrt{\frac{3}{6 m}}$

Step 2

Reduce the expression $\frac{3}{6 m}$ by cancelling the common factors.

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Step 2.1

Factor $3$ out of $3$ .

$3 \sqrt{\frac{3 (1)}{6 m}}$

Step 2.2

Factor $3$ out of $6 m$ .

$3 \sqrt{\frac{3 (1)}{3 (2 m)}}$

Step 2.3

Cancel the common factor.

$3 \sqrt{\frac{3 \cdot 1}{3 (2 m)}}$

Step 2.4

Rewrite the expression.

$3 \sqrt{\frac{1}{2 m}}$

Step 3

Rewrite $\sqrt{\frac{1}{2 m}}$ as $\frac{\sqrt{1}}{\sqrt{2 m}}$ .

$3 \frac{\sqrt{1}}{\sqrt{2 m}}$

Step 4

Any root of $1$ is $1$ .

$3 \frac{1}{\sqrt{2 m}}$

Step 5

Multiply $\frac{1}{\sqrt{2 m}}$ by $\frac{\sqrt{2 m}}{\sqrt{2 m}}$ .

$3 (\frac{1}{\sqrt{2 m}} \cdot \frac{\sqrt{2 m}}{\sqrt{2 m}})$

Step 6

Combine and simplify the denominator.

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Step 6.1

Multiply $\frac{1}{\sqrt{2 m}}$ by $\frac{\sqrt{2 m}}{\sqrt{2 m}}$ .

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

Step 6.2

Raise $\sqrt{2 m}$ to the power of $1$ .

$3 \frac{\sqrt{2 m}}{{\sqrt{2 m}}^{1} \sqrt{2 m}}$

Step 6.3

Raise $\sqrt{2 m}$ to the power of $1$ .

$3 \frac{\sqrt{2 m}}{{\sqrt{2 m}}^{1} {\sqrt{2 m}}^{1}}$

Step 6.4

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

$3 \frac{\sqrt{2 m}}{{\sqrt{2 m}}^{1 + 1}}$

Step 6.5

Add $1$ and $1$ .

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

Step 6.6

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

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Step 6.6.1

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

$3 \frac{\sqrt{2 m}}{{({(2 m)}^{\frac{1}{2}})}^{2}}$

Step 6.6.2

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

$3 \frac{\sqrt{2 m}}{{(2 m)}^{\frac{1}{2} \cdot 2}}$

Step 6.6.3

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

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

Step 6.6.4

Cancel the common factor of $2$ .

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Step 6.6.4.1

Cancel the common factor.

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

Step 6.6.4.2

Rewrite the expression.

$3 \frac{\sqrt{2 m}}{{(2 m)}^{1}}$

Step 6.6.5

Simplify.

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

Step 7

Combine $3$ and $\frac{\sqrt{2 m}}{2 m}$ .

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