Algebra Examples

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

Step 1

Combine $\sqrt{5}$ and $\sqrt{20}$ into a single radical.

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

Step 2

Cancel the common factor of $5$ and $20$ .

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Step 2.1

Factor $5$ out of $5$ .

$3 \sqrt{\frac{5 (1)}{20}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $5$ out of $20$ .

$3 \sqrt{\frac{5 \cdot 1}{5 \cdot 4}}$

Step 2.2.2

Cancel the common factor.

$3 \sqrt{\frac{5 \cdot 1}{5 \cdot 4}}$

Step 2.2.3

Rewrite the expression.

$3 \sqrt{\frac{1}{4}}$

Step 3

Rewrite $\sqrt{\frac{1}{4}}$ as $\frac{\sqrt{1}}{\sqrt{4}}$ .

$3 \frac{\sqrt{1}}{\sqrt{4}}$

Step 4

Any root of $1$ is $1$ .

$3 \frac{1}{\sqrt{4}}$

Step 5

Simplify the denominator.

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Step 5.1

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

$3 \frac{1}{\sqrt{2^{2}}}$

Step 5.2

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

$3 (\frac{1}{2})$

Step 6

Combine $3$ and $\frac{1}{2}$ .

$\frac{3}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$