Pre-Algebra Examples

$- 5 \sqrt{250 x^{7} y^{11}}$

Step 1

Rewrite $250 x^{7} y^{11}$ as ${(5 x^{3} y^{5})}^{2} \cdot (10 x y)$ .

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Step 1.1

Factor $25$ out of $250$ .

$- 5 \sqrt{25 (10) x^{7} y^{11}}$

Step 1.2

Rewrite $25$ as $5^{2}$ .

$- 5 \sqrt{5^{2} \cdot 10 x^{7} y^{11}}$

Step 1.3

Factor out $x^{6}$ .

$- 5 \sqrt{5^{2} \cdot 10 (x^{6} x) y^{11}}$

Step 1.4

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

$- 5 \sqrt{5^{2} \cdot 10 ({(x^{3})}^{2} x) y^{11}}$

Step 1.5

Factor out $y^{10}$ .

$- 5 \sqrt{5^{2} \cdot 10 ({(x^{3})}^{2} x) (y^{10} y)}$

Step 1.6

Rewrite $y^{10}$ as ${(y^{5})}^{2}$ .

$- 5 \sqrt{5^{2} \cdot 10 ({(x^{3})}^{2} x) ({(y^{5})}^{2} y)}$

Step 1.7

Move $x$ .

$- 5 \sqrt{5^{2} \cdot 10 ({(x^{3})}^{2}) {(y^{5})}^{2} x y}$

Step 1.8

Move $10$ .

$- 5 \sqrt{(5^{2} ({(x^{3})}^{2})) {(y^{5})}^{2} \cdot 10 x y}$

Step 1.9

Rewrite $(5^{2} ({(x^{3})}^{2})) {(y^{5})}^{2}$ as ${(5 x^{3} y^{5})}^{2}$ .

$- 5 \sqrt{{(5 x^{3} y^{5})}^{2} \cdot 10 x y}$

Step 1.10

Add parentheses.

$- 5 \sqrt{{(5 x^{3} y^{5})}^{2} \cdot 10 (x y)}$

Step 1.11

Add parentheses.

$- 5 \sqrt{{(5 x^{3} y^{5})}^{2} \cdot (10 x y)}$

Step 2

Pull terms out from under the radical.

$- 5 (5 x^{3} y^{5} \sqrt{10 x y})$

Step 3

Multiply $5$ by $- 5$ .

$- 25 x^{3} y^{5} \sqrt{10 x y}$