Simplify square root of (36m^2)/(4m^24)

$\sqrt{\frac{36 m^{2}}{4 m^{24}}}$

Step 1

Reduce the expression $\frac{36 m^{2}}{4 m^{24}}$ by cancelling the common factors.

Factor $4$ out of $36 m^{2}$ .

$\sqrt{\frac{4 (9 m^{2})}{4 m^{24}}}$

Factor $4$ out of $4 m^{24}$ .

$\sqrt{\frac{4 (9 m^{2})}{4 (m^{24})}}$

Cancel the common factor.

$\sqrt{\frac{4 (9 m^{2})}{4 m^{24}}}$

Rewrite the expression.

$\sqrt{\frac{9 m^{2}}{m^{24}}}$

Step 2

Cancel the common factor of $m^{2}$ and $m^{24}$ .

Factor $m^{2}$ out of $9 m^{2}$ .

$\sqrt{\frac{m^{2} \cdot 9}{m^{24}}}$

Cancel the common factors.

Factor $m^{2}$ out of $m^{24}$ .

$\sqrt{\frac{m^{2} \cdot 9}{m^{2} m^{22}}}$

Cancel the common factor.

$\sqrt{\frac{m^{2} \cdot 9}{m^{2} m^{22}}}$

Rewrite the expression.

$\sqrt{\frac{9}{m^{22}}}$

Step 3

Simplify the expression.

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

$\sqrt{\frac{3^{2}}{m^{22}}}$

Rewrite $m^{22}$ as ${(m^{11})}^{2}$ .

$\sqrt{\frac{3^{2}}{{(m^{11})}^{2}}}$

Step 4

Rewrite $\frac{3^{2}}{{(m^{11})}^{2}}$ as ${(\frac{3}{m^{11}})}^{2}$ .

$\sqrt{{(\frac{3}{m^{11}})}^{2}}$

Step 5

Pull terms out from under the radical, assuming positive real numbers.

$\frac{3}{m^{11}}$