Basic Math Examples

\frac{\sqrt{15}}{\sqrt{20}}

$\frac{\sqrt{15}}{\sqrt{20}}$

Step 1

Combine

\sqrt{15}

$\sqrt{15}$ and

\sqrt{20}

$\sqrt{20}$ into a single radical.

\sqrt{\frac{15}{20}}

$\sqrt{\frac{15}{20}}$

Step 2

Cancel the common factor of

15

$15$ and

20

$20$ .

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Step 2.1

Factor

5

$5$ out of

15

$15$ .

\sqrt{\frac{5 (3)}{20}}

$\sqrt{\frac{5 (3)}{20}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor

5

$5$ out of

20

$20$ .

\sqrt{\frac{5 \cdot 3}{5 \cdot 4}}

$\sqrt{\frac{5 \cdot 3}{5 \cdot 4}}$

Step 2.2.2

Cancel the common factor.

$\sqrt{\frac{5 \cdot 3}{5 \cdot 4}}$

Step 2.2.3

Rewrite the expression.

$\sqrt{\frac{3}{4}}$

$\sqrt{\frac{3}{4}}$

$\sqrt{\frac{3}{4}}$

Step 3

Rewrite

$\sqrt{\frac{3}{4}}$ as

$\frac{\sqrt{3}}{\sqrt{4}}$ .

$\frac{\sqrt{3}}{\sqrt{4}}$

Step 4

Simplify the denominator.

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Step 4.1

Rewrite

$4$ as

$2^{2}$ .

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

Step 4.2

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

$\frac{\sqrt{3}}{2}$

$\frac{\sqrt{3}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{3}}{2}$

Decimal Form:

$0.86602540 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$