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Simplify square root of 81m^7n^6

$\sqrt{81 m^{7} n^{6}}$

Step 1

Rewrite

$81 m^{7} n^{6}$ as

${(9 m^{3} n^{3})}^{2} m$ .

Rewrite

$81$ as

$9^{2}$ .

$\sqrt{9^{2} m^{7} n^{6}}$

Factor out

$m^{6}$ .

$\sqrt{9^{2} (m^{6} m) n^{6}}$

Rewrite

$m^{6}$ as

${(m^{3})}^{2}$ .

$\sqrt{9^{2} ({(m^{3})}^{2} m) n^{6}}$

Rewrite

$n^{6}$ as

${(n^{3})}^{2}$ .

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

Move

$m$ .

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

Rewrite

$9^{2} ({(m^{3})}^{2}) {(n^{3})}^{2}$ as

${(9 m^{3} n^{3})}^{2}$ .

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

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

Step 2

Pull terms out from under the radical.

$9 m^{3} n^{3} \sqrt{m}$

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