Algebra Examples

$\frac{\sqrt{15}}{5 \sqrt{20}}$

Step 1

Combine $\sqrt{15}$ and $\sqrt{20}$ into a single radical.

$\frac{\sqrt{\frac{15}{20}}}{5}$

Step 2

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

Tap for more steps...

Step 2.1

Factor $5$ out of $15$ .

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

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

Factor $5$ out of $20$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

Simplify the numerator.

Tap for more steps...

Step 3.1

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

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

Step 3.2

Simplify the denominator.

Tap for more steps...

Step 3.2.1

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

$\frac{\frac{\sqrt{3}}{\sqrt{2^{2}}}}{5}$

Step 3.2.2

Pull terms out from under the radical.

$\frac{\frac{\sqrt{3}}{| 2 |}}{5}$

Step 3.2.3

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

$\frac{\frac{\sqrt{3}}{2}}{5}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{\sqrt{3}}{2} \cdot \frac{1}{5}$

Step 5

Multiply $\frac{\sqrt{3}}{2} \cdot \frac{1}{5}$ .

Tap for more steps...

Step 5.1

Multiply $\frac{\sqrt{3}}{2}$ by $\frac{1}{5}$ .

$\frac{\sqrt{3}}{2 \cdot 5}$

Step 5.2

Multiply $2$ by $5$ .

$\frac{\sqrt{3}}{10}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{3}}{10}$

Decimal Form:

$0.17320508 \dots$