Algebra Examples

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

Step 1

Cancel the common factor of $15$ and $20$ .

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Step 1.1

Factor $5$ out of $15$ .

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $5$ out of $20$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 2

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

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

Step 3

Simplify the denominator.

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Step 3.1

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

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

Step 3.2

Pull terms out from under the radical.

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

Step 3.3

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.86602540 \dots$