Simplify the Radical Expression square root of 20+2 square root of 80+ square root of 72- square root of 5

$\sqrt{20} + 2 \sqrt{80} + \sqrt{72} - \sqrt{5}$

Simplify each term.

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

Factor $4$ out of $20$ .

$\sqrt{4 (5)} + 2 \sqrt{80} + \sqrt{72} - \sqrt{5}$

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

$\sqrt{2^{2} \cdot 5} + 2 \sqrt{80} + \sqrt{72} - \sqrt{5}$

Pull terms out from under the radical.

$| 2 | \sqrt{5} + 2 \sqrt{80} + \sqrt{72} - \sqrt{5}$

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

$2 \sqrt{5} + 2 \sqrt{80} + \sqrt{72} - \sqrt{5}$

Rewrite $80$ as $4^{2} \cdot 5$ .

Factor $16$ out of $80$ .

$2 \sqrt{5} + 2 \sqrt{16 (5)} + \sqrt{72} - \sqrt{5}$

Rewrite $16$ as $4^{2}$ .

$2 \sqrt{5} + 2 \sqrt{4^{2} \cdot 5} + \sqrt{72} - \sqrt{5}$

Pull terms out from under the radical.

$2 \sqrt{5} + 2 (| 4 | \sqrt{5}) + \sqrt{72} - \sqrt{5}$

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

$2 \sqrt{5} + 2 (4 \sqrt{5}) + \sqrt{72} - \sqrt{5}$

Multiply $4$ by $2$ .

$2 \sqrt{5} + 8 \sqrt{5} + \sqrt{72} - \sqrt{5}$

Rewrite $72$ as $6^{2} \cdot 2$ .

Factor $36$ out of $72$ .

$2 \sqrt{5} + 8 \sqrt{5} + \sqrt{36 (2)} - \sqrt{5}$

Rewrite $36$ as $6^{2}$ .

$2 \sqrt{5} + 8 \sqrt{5} + \sqrt{6^{2} \cdot 2} - \sqrt{5}$

Pull terms out from under the radical.

$2 \sqrt{5} + 8 \sqrt{5} + | 6 | \sqrt{2} - \sqrt{5}$

The absolute value is the distance between a number and zero. The distance between $0$ and $6$ is $6$ .

$2 \sqrt{5} + 8 \sqrt{5} + 6 \sqrt{2} - \sqrt{5}$

Add $2 \sqrt{5}$ and $8 \sqrt{5}$ .

$10 \sqrt{5} + 6 \sqrt{2} - \sqrt{5}$

Subtract $\sqrt{5}$ from $10 \sqrt{5}$ .

$9 \sqrt{5} + 6 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$9 \sqrt{5} + 6 \sqrt{2}$

Decimal Form:

$28.60989317 \dots$