Simplify square root of -180x^16

$\sqrt{- 180 x^{16}}$

Step 1

Rewrite $- 180 x^{16}$ as ${(6 x^{8})}^{2} \cdot - 5$ .

Factor $36$ out of $- 180$ .

$\sqrt{36 (- 5) x^{16}}$

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

$\sqrt{6^{2} \cdot - 5 x^{16}}$

Rewrite $x^{16}$ as ${(x^{8})}^{2}$ .

$\sqrt{6^{2} \cdot - 5 {(x^{8})}^{2}}$

Move $- 5$ .

$\sqrt{6^{2} {(x^{8})}^{2} \cdot - 5}$

Rewrite $6^{2} {(x^{8})}^{2}$ as ${(6 x^{8})}^{2}$ .

$\sqrt{{(6 x^{8})}^{2} \cdot - 5}$

Step 2

Pull terms out from under the radical.

$6 x^{8} \sqrt{- 5}$

Step 3

Rewrite $- 5$ as $- 1 (5)$ .

$6 x^{8} \sqrt{- 1 (5)}$

Step 4

Rewrite $\sqrt{- 1 (5)}$ as $\sqrt{- 1} \cdot \sqrt{5}$ .

$6 x^{8} (\sqrt{- 1} \cdot \sqrt{5})$

Step 5

Rewrite $\sqrt{- 1}$ as $i$ .

$6 x^{8} i \sqrt{5}$