Algebra Examples

$\frac{\sqrt{72}}{\sqrt{36 x^{8} y^{2}}}$

Step 1

Combine $\sqrt{72}$ and $\sqrt{36 x^{8} y^{2}}$ into a single radical.

$\sqrt{\frac{72}{36 x^{8} y^{2}}}$

Step 2

Reduce the expression $\frac{72}{36 x^{8} y^{2}}$ by cancelling the common factors.

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Step 2.1

Factor $36$ out of $72$ .

$\sqrt{\frac{36 \cdot 2}{36 x^{8} y^{2}}}$

Step 2.2

Factor $36$ out of $36 x^{8} y^{2}$ .

$\sqrt{\frac{36 \cdot 2}{36 (x^{8} y^{2})}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{36 \cdot 2}{36 (x^{8} y^{2})}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{2}{x^{8} y^{2}}}$

Step 3

Rewrite $\frac{2}{x^{8} y^{2}}$ as ${(\frac{1}{x^{4} y})}^{2} \cdot 2$ .

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Step 3.1

Factor the perfect power $1^{2}$ out of $2$ .

$\sqrt{\frac{1^{2} \cdot 2}{x^{8} y^{2}}}$

Step 3.2

Factor the perfect power ${(x^{4} y)}^{2}$ out of $x^{8} y^{2}$ .

$\sqrt{\frac{1^{2} \cdot 2}{{(x^{4} y)}^{2} \cdot 1}}$

Step 3.3

Rearrange the fraction $\frac{1^{2} \cdot 2}{{(x^{4} y)}^{2} \cdot 1}$ .

$\sqrt{{(\frac{1}{x^{4} y})}^{2} \cdot 2}$

Step 4

Pull terms out from under the radical.

$\frac{1}{x^{4} y} \sqrt{2}$

Step 5

Combine $\frac{1}{x^{4} y}$ and $\sqrt{2}$ .

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