Algebra Examples

$\frac{\sqrt{20 x^{7} y^{10}}}{\sqrt{y^{2}}}$

Step 1

Combine $\sqrt{20 x^{7} y^{10}}$ and $\sqrt{y^{2}}$ into a single radical.

$\sqrt{\frac{20 x^{7} y^{10}}{y^{2}}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Reduce the expression $\frac{20 x^{7} y^{10}}{y^{2}}$ by cancelling the common factors.

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Step 2.1.1

Factor $y^{2}$ out of $20 x^{7} y^{10}$ .

$\sqrt{\frac{y^{2} (20 x^{7} y^{8})}{y^{2}}}$

Step 2.1.2

Multiply by $1$ .

$\sqrt{\frac{y^{2} (20 x^{7} y^{8})}{y^{2} \cdot 1}}$

Step 2.1.3

Cancel the common factor.

$\sqrt{\frac{y^{2} (20 x^{7} y^{8})}{y^{2} \cdot 1}}$

Step 2.1.4

Rewrite the expression.

$\sqrt{\frac{20 x^{7} y^{8}}{1}}$

Step 2.2

Divide $20 x^{7} y^{8}$ by $1$ .

$\sqrt{20 x^{7} y^{8}}$

Step 3

Rewrite $20 x^{7} y^{8}$ as ${(2 x^{3} y^{4})}^{2} \cdot (5 x)$ .

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Step 3.1

Factor $4$ out of $20$ .

$\sqrt{4 (5) x^{7} y^{8}}$

Step 3.2

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

$\sqrt{2^{2} \cdot 5 x^{7} y^{8}}$

Step 3.3

Factor out $x^{6}$ .

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

Step 3.4

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

$\sqrt{2^{2} \cdot 5 ({(x^{3})}^{2} x) y^{8}}$

Step 3.5

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

$\sqrt{2^{2} \cdot 5 ({(x^{3})}^{2} x) {(y^{4})}^{2}}$

Step 3.6

Move $x$ .

$\sqrt{2^{2} \cdot 5 ({(x^{3})}^{2}) {(y^{4})}^{2} x}$

Step 3.7

Move $5$ .

$\sqrt{(2^{2} ({(x^{3})}^{2})) {(y^{4})}^{2} \cdot 5 x}$

Step 3.8

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

$\sqrt{{(2 x^{3} y^{4})}^{2} \cdot 5 x}$

Step 3.9

Add parentheses.

$\sqrt{{(2 x^{3} y^{4})}^{2} \cdot (5 x)}$

Step 4

Pull terms out from under the radical.

$2 x^{3} y^{4} \sqrt{5 x}$