Algebra Examples

$- \sqrt{- 25 x^{12} y^{8}}$

Step 1

Rewrite $- 25 x^{12} y^{8}$ as ${(5 x^{6} y^{4})}^{2} \cdot - 1$ .

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Step 1.1

Factor $25$ out of $- 25$ .

$- \sqrt{25 (- 1) x^{12} y^{8}}$

Step 1.2

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

$- \sqrt{5^{2} \cdot - 1 x^{12} y^{8}}$

Step 1.3

Rewrite $x^{12}$ as ${(x^{6})}^{2}$ .

$- \sqrt{5^{2} \cdot - 1 {(x^{6})}^{2} y^{8}}$

Step 1.4

Rewrite $y^{8}$ as ${(y^{4})}^{2}$ .

$- \sqrt{5^{2} \cdot - 1 {(x^{6})}^{2} {(y^{4})}^{2}}$

Step 1.5

Move $- 1$ .

$- \sqrt{5^{2} {(x^{6})}^{2} {(y^{4})}^{2} \cdot - 1}$

Step 1.6

Rewrite $5^{2} {(x^{6})}^{2} {(y^{4})}^{2}$ as ${(5 x^{6} y^{4})}^{2}$ .

$- \sqrt{{(5 x^{6} y^{4})}^{2} \cdot - 1}$

Step 2

Pull terms out from under the radical.

$- (5 x^{6} y^{4} \sqrt{- 1})$

Step 3

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

$- (5 x^{6} y^{4} i)$

Step 4

Multiply $5$ by $- 1$ .

$- 5 x^{6} y^{4} i$