Finite Math Examples

$\frac{\sqrt{18 x^{5} y^{14}}}{\sqrt{32 x y^{2}}}$

Step 1

Combine $\sqrt{18 x^{5} y^{14}}$ and $\sqrt{32 x y^{2}}$ into a single radical.

$\sqrt{\frac{18 x^{5} y^{14}}{32 x y^{2}}}$

Step 2

Reduce the expression $\frac{18 x^{5} y^{14}}{32 x y^{2}}$ by cancelling the common factors.

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Step 2.1

Factor $2$ out of $18 x^{5} y^{14}$ .

$\sqrt{\frac{2 (9 x^{5} y^{14})}{32 x y^{2}}}$

Step 2.2

Factor $2$ out of $32 x y^{2}$ .

$\sqrt{\frac{2 (9 x^{5} y^{14})}{2 (16 x y^{2})}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{2 (9 x^{5} y^{14})}{2 (16 x y^{2})}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{9 x^{5} y^{14}}{16 x y^{2}}}$

Step 3

Cancel the common factor of $x^{5}$ and $x$ .

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Step 3.1

Factor $x$ out of $9 x^{5} y^{14}$ .

$\sqrt{\frac{x (9 x^{4} y^{14})}{16 x y^{2}}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $x$ out of $16 x y^{2}$ .

$\sqrt{\frac{x (9 x^{4} y^{14})}{x (16 y^{2})}}$

Step 3.2.2

Cancel the common factor.

$\sqrt{\frac{x (9 x^{4} y^{14})}{x (16 y^{2})}}$

Step 3.2.3

Rewrite the expression.

$\sqrt{\frac{9 x^{4} y^{14}}{16 y^{2}}}$

Step 4

Cancel the common factor of $y^{14}$ and $y^{2}$ .

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Step 4.1

Factor $y^{2}$ out of $9 x^{4} y^{14}$ .

$\sqrt{\frac{y^{2} (9 x^{4} y^{12})}{16 y^{2}}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $y^{2}$ out of $16 y^{2}$ .

$\sqrt{\frac{y^{2} (9 x^{4} y^{12})}{y^{2} \cdot 16}}$

Step 4.2.2

Cancel the common factor.

$\sqrt{\frac{y^{2} (9 x^{4} y^{12})}{y^{2} \cdot 16}}$

Step 4.2.3

Rewrite the expression.

$\sqrt{\frac{9 x^{4} y^{12}}{16}}$

Step 5

Rewrite $9 x^{4} y^{12}$ as ${(3 x^{2} y^{6})}^{2}$ .

$\sqrt{\frac{{(3 x^{2} y^{6})}^{2}}{16}}$

Step 6

Rewrite $16$ as $4^{2}$ .

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

Step 7

Rewrite $\frac{{(3 x^{2} y^{6})}^{2}}{4^{2}}$ as ${(\frac{3 x^{2} y^{6}}{4})}^{2}$ .

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

Step 8

Pull terms out from under the radical, assuming positive real numbers.

$\frac{3 x^{2} y^{6}}{4}$