Algebra Examples

$\frac{\sqrt{180 x^{2} y^{5}}}{\sqrt{10 x^{2}}}$

Step 1

Combine $\sqrt{180 x^{2} y^{5}}$ and $\sqrt{10 x^{2}}$ into a single radical.

$\sqrt{\frac{180 x^{2} y^{5}}{10 x^{2}}}$

Step 2

Reduce the expression $\frac{180 x^{2} y^{5}}{10 x^{2}}$ by cancelling the common factors.

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Step 2.1

Factor $10$ out of $180 x^{2} y^{5}$ .

$\sqrt{\frac{10 (18 x^{2} y^{5})}{10 x^{2}}}$

Step 2.2

Factor $10$ out of $10 x^{2}$ .

$\sqrt{\frac{10 (18 x^{2} y^{5})}{10 (x^{2})}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{10 (18 x^{2} y^{5})}{10 x^{2}}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{18 x^{2} y^{5}}{x^{2}}}$

Step 3

Cancel the common factor of $x^{2}$ .

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Step 3.1

Cancel the common factor.

$\sqrt{\frac{18 x^{2} y^{5}}{x^{2}}}$

Step 3.2

Divide $18 y^{5}$ by $1$ .

$\sqrt{18 y^{5}}$

Step 4

Rewrite $18 y^{5}$ as ${(3 y^{2})}^{2} \cdot (2 y)$ .

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Step 4.1

Factor $9$ out of $18$ .

$\sqrt{9 (2) y^{5}}$

Step 4.2

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 2 y^{5}}$

Step 4.3

Factor out $y^{4}$ .

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

Step 4.4

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

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

Step 4.5

Move $2$ .

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

Step 4.6

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

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

Step 4.7

Add parentheses.

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

Step 5

Pull terms out from under the radical.

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