Pre-Algebra Examples

$3 \sqrt{- 81 m^{4} n^{10}}$

Step 1

Rewrite $- 81 m^{4} n^{10}$ as ${(9 m^{2} n^{5})}^{2} \cdot - 1$ .

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Step 1.1

Factor $81$ out of $- 81$ .

$3 \sqrt{81 (- 1) m^{4} n^{10}}$

Step 1.2

Rewrite $81$ as $9^{2}$ .

$3 \sqrt{9^{2} \cdot - 1 m^{4} n^{10}}$

Step 1.3

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

$3 \sqrt{9^{2} \cdot - 1 {(m^{2})}^{2} n^{10}}$

Step 1.4

Rewrite $n^{10}$ as ${(n^{5})}^{2}$ .

$3 \sqrt{9^{2} \cdot - 1 {(m^{2})}^{2} {(n^{5})}^{2}}$

Step 1.5

Move $- 1$ .

$3 \sqrt{9^{2} {(m^{2})}^{2} {(n^{5})}^{2} \cdot - 1}$

Step 1.6

Rewrite $9^{2} {(m^{2})}^{2} {(n^{5})}^{2}$ as ${(9 m^{2} n^{5})}^{2}$ .

$3 \sqrt{{(9 m^{2} n^{5})}^{2} \cdot - 1}$

Step 2

Pull terms out from under the radical.

$3 (9 m^{2} n^{5} \sqrt{- 1})$

Step 3

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

$3 (9 m^{2} n^{5} i)$

Step 4

Multiply $9$ by $3$ .

$27 m^{2} n^{5} i$