Pre-Algebra Examples

$3 \sqrt{- 64 a^{8} b^{5}}$

Step 1

Rewrite $- 64 a^{8} b^{5}$ as ${(8 a^{4} b^{2})}^{2} \cdot (- b)$ .

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Step 1.1

Factor $64$ out of $- 64$ .

$3 \sqrt{64 (- 1) a^{8} b^{5}}$

Step 1.2

Rewrite $64$ as $8^{2}$ .

$3 \sqrt{8^{2} \cdot - 1 a^{8} b^{5}}$

Step 1.3

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

$3 \sqrt{8^{2} \cdot - 1 {(a^{4})}^{2} b^{5}}$

Step 1.4

Factor out $b^{4}$ .

$3 \sqrt{8^{2} \cdot - 1 {(a^{4})}^{2} (b^{4} b)}$

Step 1.5

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

$3 \sqrt{8^{2} \cdot - 1 {(a^{4})}^{2} ({(b^{2})}^{2} b)}$

Step 1.6

Move $- 1$ .

$3 \sqrt{8^{2} {(a^{4})}^{2} {(b^{2})}^{2} \cdot - 1 b}$

Step 1.7

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

$3 \sqrt{{(8 a^{4} b^{2})}^{2} \cdot - 1 b}$

Step 1.8

Add parentheses.

$3 \sqrt{{(8 a^{4} b^{2})}^{2} \cdot (- b)}$

Step 2

Pull terms out from under the radical.

$3 (8 a^{4} b^{2} \sqrt{- b})$

Step 3

Multiply $8$ by $3$ .

$24 a^{4} b^{2} \sqrt{- b}$