Finite Math Examples

$\frac{\sqrt{60 x^{10} y^{10}}}{\sqrt{5 x^{2} y^{3}}}$

Step 1

Combine $\sqrt{60 x^{10} y^{10}}$ and $\sqrt{5 x^{2} y^{3}}$ into a single radical.

$\sqrt{\frac{60 x^{10} y^{10}}{5 x^{2} y^{3}}}$

Step 2

Reduce the expression $\frac{60 x^{10} y^{10}}{5 x^{2} y^{3}}$ by cancelling the common factors.

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Step 2.1

Factor $5$ out of $60 x^{10} y^{10}$ .

$\sqrt{\frac{5 (12 x^{10} y^{10})}{5 x^{2} y^{3}}}$

Step 2.2

Factor $5$ out of $5 x^{2} y^{3}$ .

$\sqrt{\frac{5 (12 x^{10} y^{10})}{5 (x^{2} y^{3})}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{5 (12 x^{10} y^{10})}{5 (x^{2} y^{3})}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{12 x^{10} y^{10}}{x^{2} y^{3}}}$

Step 3

Cancel the common factor of $x^{10}$ and $x^{2}$ .

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Step 3.1

Factor $x^{2}$ out of $12 x^{10} y^{10}$ .

$\sqrt{\frac{x^{2} (12 x^{8} y^{10})}{x^{2} y^{3}}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $x^{2}$ out of $x^{2} y^{3}$ .

$\sqrt{\frac{x^{2} (12 x^{8} y^{10})}{x^{2} (y^{3})}}$

Step 3.2.2

Cancel the common factor.

$\sqrt{\frac{x^{2} (12 x^{8} y^{10})}{x^{2} y^{3}}}$

Step 3.2.3

Rewrite the expression.

$\sqrt{\frac{12 x^{8} y^{10}}{y^{3}}}$

Step 4

Cancel the common factor of $y^{10}$ and $y^{3}$ .

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Step 4.1

Factor $y^{3}$ out of $12 x^{8} y^{10}$ .

$\sqrt{\frac{y^{3} (12 x^{8} y^{7})}{y^{3}}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Multiply by $1$ .

$\sqrt{\frac{y^{3} (12 x^{8} y^{7})}{y^{3} \cdot 1}}$

Step 4.2.2

Cancel the common factor.

$\sqrt{\frac{y^{3} (12 x^{8} y^{7})}{y^{3} \cdot 1}}$

Step 4.2.3

Rewrite the expression.

$\sqrt{\frac{12 x^{8} y^{7}}{1}}$

Step 4.2.4

Divide $12 x^{8} y^{7}$ by $1$ .

$\sqrt{12 x^{8} y^{7}}$

Step 5

Rewrite $12 x^{8} y^{7}$ as ${(2 x^{4} y^{3})}^{2} \cdot (3 y)$ .

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Step 5.1

Factor $4$ out of $12$ .

$\sqrt{4 (3) x^{8} y^{7}}$

Step 5.2

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

$\sqrt{2^{2} \cdot 3 x^{8} y^{7}}$

Step 5.3

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

$\sqrt{2^{2} \cdot 3 {(x^{4})}^{2} y^{7}}$

Step 5.4

Factor out $y^{6}$ .

$\sqrt{2^{2} \cdot 3 {(x^{4})}^{2} (y^{6} y)}$

Step 5.5

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

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

Step 5.6

Move $3$ .

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

Step 5.7

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

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

Step 5.8

Add parentheses.

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

Step 6

Pull terms out from under the radical.

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