Algebra Examples

$\frac{\sqrt{405 x^{10} y^{7}}}{\sqrt{9 x^{4}}}$

Step 1

Combine $\sqrt{405 x^{10} y^{7}}$ and $\sqrt{9 x^{4}}$ into a single radical.

$\sqrt{\frac{405 x^{10} y^{7}}{9 x^{4}}}$

Step 2

Reduce the expression $\frac{405 x^{10} y^{7}}{9 x^{4}}$ by cancelling the common factors.

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Step 2.1

Factor $9$ out of $405 x^{10} y^{7}$ .

$\sqrt{\frac{9 (45 x^{10} y^{7})}{9 x^{4}}}$

Step 2.2

Factor $9$ out of $9 x^{4}$ .

$\sqrt{\frac{9 (45 x^{10} y^{7})}{9 (x^{4})}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{9 (45 x^{10} y^{7})}{9 x^{4}}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{45 x^{10} y^{7}}{x^{4}}}$

Step 3

Cancel the common factor of $x^{10}$ and $x^{4}$ .

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Step 3.1

Factor $x^{4}$ out of $45 x^{10} y^{7}$ .

$\sqrt{\frac{x^{4} (45 x^{6} y^{7})}{x^{4}}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\sqrt{\frac{x^{4} (45 x^{6} y^{7})}{x^{4} \cdot 1}}$

Step 3.2.2

Cancel the common factor.

$\sqrt{\frac{x^{4} (45 x^{6} y^{7})}{x^{4} \cdot 1}}$

Step 3.2.3

Rewrite the expression.

$\sqrt{\frac{45 x^{6} y^{7}}{1}}$

Step 3.2.4

Divide $45 x^{6} y^{7}$ by $1$ .

$\sqrt{45 x^{6} y^{7}}$

Step 4

Rewrite $45 x^{6} y^{7}$ as ${(3 x^{3} y^{3})}^{2} \cdot (5 y)$ .

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Step 4.1

Factor $9$ out of $45$ .

$\sqrt{9 (5) x^{6} y^{7}}$

Step 4.2

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

$\sqrt{3^{2} \cdot 5 x^{6} y^{7}}$

Step 4.3

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

$\sqrt{3^{2} \cdot 5 {(x^{3})}^{2} y^{7}}$

Step 4.4

Factor out $y^{6}$ .

$\sqrt{3^{2} \cdot 5 {(x^{3})}^{2} (y^{6} y)}$

Step 4.5

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

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

Step 4.6

Move $5$ .

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

Step 4.7

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

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

Step 4.8

Add parentheses.

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

Step 5

Pull terms out from under the radical.

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