Simplify the Radical Expression square root of 20- square root of 5

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

Step 1

Simplify each term.

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

Factor $4$ out of $20$ .

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

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

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

Pull terms out from under the radical.

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

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

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

Step 2

Subtract $\sqrt{5}$ from $2 \sqrt{5}$ .

$\sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{5}$

Decimal Form:

$2.23606797 \dots$