Simplify square root of (36a^8)/(225a^2)

$\sqrt{\frac{36 a^{8}}{225 a^{2}}}$

Step 1

Reduce the expression $\frac{36 a^{8}}{225 a^{2}}$ by cancelling the common factors.

Factor $9$ out of $36 a^{8}$ .

$\sqrt{\frac{9 (4 a^{8})}{225 a^{2}}}$

Factor $9$ out of $225 a^{2}$ .

$\sqrt{\frac{9 (4 a^{8})}{9 (25 a^{2})}}$

Cancel the common factor.

$\sqrt{\frac{9 (4 a^{8})}{9 (25 a^{2})}}$

Rewrite the expression.

$\sqrt{\frac{4 a^{8}}{25 a^{2}}}$

Step 2

Cancel the common factor of $a^{8}$ and $a^{2}$ .

Factor $a^{2}$ out of $4 a^{8}$ .

$\sqrt{\frac{a^{2} (4 a^{6})}{25 a^{2}}}$

Cancel the common factors.

Factor $a^{2}$ out of $25 a^{2}$ .

$\sqrt{\frac{a^{2} (4 a^{6})}{a^{2} \cdot 25}}$

Cancel the common factor.

$\sqrt{\frac{a^{2} (4 a^{6})}{a^{2} \cdot 25}}$

Rewrite the expression.

$\sqrt{\frac{4 a^{6}}{25}}$

Step 3

Rewrite $4 a^{6}$ as ${(2 a^{3})}^{2}$ .

$\sqrt{\frac{{(2 a^{3})}^{2}}{25}}$

Step 4

Rewrite $25$ as $5^{2}$ .

$\sqrt{\frac{{(2 a^{3})}^{2}}{5^{2}}}$

Step 5

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

$\sqrt{{(\frac{2 a^{3}}{5})}^{2}}$

Step 6

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

$\frac{2 a^{3}}{5}$