Simplify Simplify - square root of -121a^4b^2

Simplify $- \sqrt{- 121 a^{4} b^{2}}$

Step 1

Rewrite $- 121 a^{4} b^{2}$ as ${(11 a^{2} b)}^{2} \cdot - 1$ .

Factor $121$ out of $- 121$ .

$- \sqrt{121 (- 1) a^{4} b^{2}}$

Rewrite $121$ as $11^{2}$ .

$- \sqrt{11^{2} \cdot - 1 a^{4} b^{2}}$

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

$- \sqrt{11^{2} \cdot - 1 {(a^{2})}^{2} b^{2}}$

Move $- 1$ .

$- \sqrt{11^{2} {(a^{2})}^{2} b^{2} \cdot - 1}$

Rewrite $11^{2} {(a^{2})}^{2} b^{2}$ as ${(11 a^{2} b)}^{2}$ .

$- \sqrt{{(11 a^{2} b)}^{2} \cdot - 1}$

Step 2

Pull terms out from under the radical.

$- (11 a^{2} b \sqrt{- 1})$

Step 3

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

$- (11 a^{2} b i)$

Step 4

Multiply $11$ by $- 1$ .

$- 11 a^{2} b i$