Simplify square root of (72x^16)/(50x^36)

$\sqrt{\frac{72 x^{16}}{50 x^{36}}}$

Reduce the expression $\frac{72 x^{16}}{50 x^{36}}$ by cancelling the common factors.

Factor $2$ out of $72 x^{16}$ .

$\sqrt{\frac{2 (36 x^{16})}{50 x^{36}}}$

Factor $2$ out of $50 x^{36}$ .

$\sqrt{\frac{2 (36 x^{16})}{2 (25 x^{36})}}$

Cancel the common factor.

$\sqrt{\frac{2 (36 x^{16})}{2 (25 x^{36})}}$

Rewrite the expression.

$\sqrt{\frac{36 x^{16}}{25 x^{36}}}$

Cancel the common factor of $x^{16}$ and $x^{36}$ .

Factor $x^{16}$ out of $36 x^{16}$ .

$\sqrt{\frac{x^{16} \cdot 36}{25 x^{36}}}$

Cancel the common factors.

Factor $x^{16}$ out of $25 x^{36}$ .

$\sqrt{\frac{x^{16} \cdot 36}{x^{16} (25 x^{20})}}$

Cancel the common factor.

$\sqrt{\frac{x^{16} \cdot 36}{x^{16} (25 x^{20})}}$

Rewrite the expression.

$\sqrt{\frac{36}{25 x^{20}}}$

Rewrite $36$ as $6^{2}$ .

$\sqrt{\frac{6^{2}}{25 x^{20}}}$

Rewrite $25 x^{20}$ as ${(5 x^{10})}^{2}$ .

$\sqrt{\frac{6^{2}}{{(5 x^{10})}^{2}}}$

Rewrite $\frac{6^{2}}{{(5 x^{10})}^{2}}$ as ${(\frac{6}{5 x^{10}})}^{2}$ .

$\sqrt{{(\frac{6}{5 x^{10}})}^{2}}$

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

$\frac{6}{5 x^{10}}$