Algebra Examples

$\sqrt{180 x^{8} y^{19}}$

Step 1

Rewrite $180 x^{8} y^{19}$ as ${(6 x^{4} y^{9})}^{2} \cdot (5 y)$ .

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Step 1.1

Factor $36$ out of $180$ .

$\sqrt{36 (5) x^{8} y^{19}}$

Step 1.2

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2} \cdot 5 x^{8} y^{19}}$

Step 1.3

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

$\sqrt{6^{2} \cdot 5 {(x^{4})}^{2} y^{19}}$

Step 1.4

Factor out $y^{18}$ .

$\sqrt{6^{2} \cdot 5 {(x^{4})}^{2} (y^{18} y)}$

Step 1.5

Rewrite $y^{18}$ as ${(y^{9})}^{2}$ .

$\sqrt{6^{2} \cdot 5 {(x^{4})}^{2} ({(y^{9})}^{2} y)}$

Step 1.6

Move $5$ .

$\sqrt{6^{2} {(x^{4})}^{2} {(y^{9})}^{2} \cdot 5 y}$

Step 1.7

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

$\sqrt{{(6 x^{4} y^{9})}^{2} \cdot 5 y}$

Step 1.8

Add parentheses.

$\sqrt{{(6 x^{4} y^{9})}^{2} \cdot (5 y)}$

Step 2

Pull terms out from under the radical.

$6 x^{4} y^{9} \sqrt{5 y}$