Algebra Examples

$\sqrt{8 x^{7} y^{8}}$

Step 1

Rewrite $8 x^{7} y^{8}$ as ${(2 x^{3} y^{4})}^{2} \cdot (2 x)$ .

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Step 1.1

Factor $4$ out of $8$ .

$\sqrt{4 (2) x^{7} y^{8}}$

Step 1.2

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

$\sqrt{2^{2} \cdot 2 x^{7} y^{8}}$

Step 1.3

Factor out $x^{6}$ .

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

Step 1.4

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

$\sqrt{2^{2} \cdot 2 ({(x^{3})}^{2} x) y^{8}}$

Step 1.5

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

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

Step 1.6

Move $x$ .

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

Step 1.7

Move $2$ .

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

Step 1.8

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

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

Step 1.9

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$2 x^{3} y^{4} \sqrt{2 x}$