Algebra Examples

$\sqrt{20} + \sqrt{45} - \sqrt{5}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $20$ as $2^{2} \cdot 5$ .

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Step 1.1.1

Factor $4$ out of $20$ .

$\sqrt{4 (5)} + \sqrt{45} - \sqrt{5}$

Step 1.1.2

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

$\sqrt{2^{2} \cdot 5} + \sqrt{45} - \sqrt{5}$

Step 1.2

Pull terms out from under the radical.

$| 2 | \sqrt{5} + \sqrt{45} - \sqrt{5}$

Step 1.3

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

$2 \sqrt{5} + \sqrt{45} - \sqrt{5}$

Step 1.4

Rewrite $45$ as $3^{2} \cdot 5$ .

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Step 1.4.1

Factor $9$ out of $45$ .

$2 \sqrt{5} + \sqrt{9 (5)} - \sqrt{5}$

Step 1.4.2

Rewrite $9$ as $3^{2}$ .

$2 \sqrt{5} + \sqrt{3^{2} \cdot 5} - \sqrt{5}$

Step 1.5

Pull terms out from under the radical.

$2 \sqrt{5} + | 3 | \sqrt{5} - \sqrt{5}$

Step 1.6

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$2 \sqrt{5} + 3 \sqrt{5} - \sqrt{5}$

Step 2

Add $2 \sqrt{5}$ and $3 \sqrt{5}$ .

$5 \sqrt{5} - \sqrt{5}$

Step 3

Subtract $\sqrt{5}$ from $5 \sqrt{5}$ .

$4 \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{5}$

Decimal Form:

$8.94427190 \dots$