Simplify the Radical Expression square root of 20+ square root of 45

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

Simplify each term.

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

Factor $4$ out of $20$ .

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

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

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

Pull terms out from under the radical.

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

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

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

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

Factor $9$ out of $45$ .

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

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

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

Pull terms out from under the radical.

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

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

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

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

$5 \sqrt{5}$

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{5}$

Decimal Form:

$11.18033988 \dots$