Finite Math Examples

$9 \sqrt{32 x^{12} y^{12}}$

Step 1

Rewrite $32 x^{12} y^{12}$ as ${(4 x^{6} y^{6})}^{2} \cdot 2$ .

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Step 1.1

Factor $16$ out of $32$ .

$9 \sqrt{16 (2) x^{12} y^{12}}$

Step 1.2

Rewrite $16$ as $4^{2}$ .

$9 \sqrt{4^{2} \cdot 2 x^{12} y^{12}}$

Step 1.3

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

$9 \sqrt{4^{2} \cdot 2 {(x^{6})}^{2} y^{12}}$

Step 1.4

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

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

Step 1.5

Move $2$ .

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

Step 1.6

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $4$ by $9$ .

$36 x^{6} y^{6} \sqrt{2}$