Algebra Examples

$- \sqrt{252 x^{6} y^{15}}$

Step 1

Rewrite $252 x^{6} y^{15}$ as ${(6 x^{3} y^{7})}^{2} \cdot (7 y)$ .

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Step 1.1

Factor $36$ out of $252$ .

$- \sqrt{36 (7) x^{6} y^{15}}$

Step 1.2

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

$- \sqrt{6^{2} \cdot 7 x^{6} y^{15}}$

Step 1.3

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

$- \sqrt{6^{2} \cdot 7 {(x^{3})}^{2} y^{15}}$

Step 1.4

Factor out $y^{14}$ .

$- \sqrt{6^{2} \cdot 7 {(x^{3})}^{2} (y^{14} y)}$

Step 1.5

Rewrite $y^{14}$ as ${(y^{7})}^{2}$ .

$- \sqrt{6^{2} \cdot 7 {(x^{3})}^{2} ({(y^{7})}^{2} y)}$

Step 1.6

Move $7$ .

$- \sqrt{6^{2} {(x^{3})}^{2} {(y^{7})}^{2} \cdot 7 y}$

Step 1.7

Rewrite $6^{2} {(x^{3})}^{2} {(y^{7})}^{2}$ as ${(6 x^{3} y^{7})}^{2}$ .

$- \sqrt{{(6 x^{3} y^{7})}^{2} \cdot 7 y}$

Step 1.8

Add parentheses.

$- \sqrt{{(6 x^{3} y^{7})}^{2} \cdot (7 y)}$

Step 2

Pull terms out from under the radical.

$- (6 x^{3} y^{7} \sqrt{7 y})$

Step 3

Multiply $6$ by $- 1$ .

$- 6 x^{3} y^{7} \sqrt{7 y}$