Simplify square root of 27/(m^5)

$\sqrt{\frac{27}{m^{5}}}$

Step 1

Rewrite $\frac{27}{m^{5}}$ as ${(\frac{3}{m^{2}})}^{2} \frac{3}{m}$ .

Factor the perfect power $3^{2}$ out of $27$ .

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

Factor the perfect power ${(m^{2})}^{2}$ out of $m^{5}$ .

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

Rearrange the fraction $\frac{3^{2} \cdot 3}{{(m^{2})}^{2} m}$ .

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite $\sqrt{\frac{3}{m}}$ as $\frac{\sqrt{3}}{\sqrt{m}}$ .

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

Step 4

Combine.

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

Step 5

Multiply $\frac{3 \sqrt{3}}{m^{2} \sqrt{m}}$ by $\frac{\sqrt{m}}{\sqrt{m}}$ .

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

Step 6

Combine and simplify the denominator.

Multiply $\frac{3 \sqrt{3}}{m^{2} \sqrt{m}}$ by $\frac{\sqrt{m}}{\sqrt{m}}$ .

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

Move $\sqrt{m}$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Step 7

Multiply $m^{2}$ by $m$ by adding the exponents.

Multiply $m^{2}$ by $m$ .

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

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

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

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

Add $2$ and $1$ .

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

Step 8

Combine using the product rule for radicals.

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

Step 9

Move $3$ to the left of $m$ .

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

Simplify square root of 27/(m^5)

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