Basic Math Examples

$\sqrt{81 x^{9} y^{6}}$

Step 1

Rewrite $81 x^{9} y^{6}$ as ${(9 x^{4} y^{3})}^{2} x$ .

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Step 1.1

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

$\sqrt{9^{2} x^{9} y^{6}}$

Step 1.2

Factor out $x^{8}$ .

$\sqrt{9^{2} (x^{8} x) y^{6}}$

Step 1.3

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

$\sqrt{9^{2} ({(x^{4})}^{2} x) y^{6}}$

Step 1.4

Rewrite $y^{6}$ as ${(y^{3})}^{2}$ .

$\sqrt{9^{2} ({(x^{4})}^{2} x) {(y^{3})}^{2}}$

Step 1.5

Move $x$ .

$\sqrt{9^{2} ({(x^{4})}^{2}) {(y^{3})}^{2} x}$

Step 1.6

Rewrite $9^{2} ({(x^{4})}^{2}) {(y^{3})}^{2}$ as ${(9 x^{4} y^{3})}^{2}$ .

$\sqrt{{(9 x^{4} y^{3})}^{2} x}$

Step 2

Pull terms out from under the radical.

$9 x^{4} y^{3} \sqrt{x}$