Simplify the Radical Expression -3 square root of 12+3 square root of 3+3 square root of 20

$- 3 \sqrt{12} + 3 \sqrt{3} + 3 \sqrt{20}$

Step 1

Simplify each term.

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$- 3 \sqrt{4 (3)} + 3 \sqrt{3} + 3 \sqrt{20}$

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

$- 3 \sqrt{2^{2} \cdot 3} + 3 \sqrt{3} + 3 \sqrt{20}$

Pull terms out from under the radical.

$- 3 (| 2 | \sqrt{3}) + 3 \sqrt{3} + 3 \sqrt{20}$

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

$- 3 (2 \sqrt{3}) + 3 \sqrt{3} + 3 \sqrt{20}$

Multiply $2$ by $- 3$ .

$- 6 \sqrt{3} + 3 \sqrt{3} + 3 \sqrt{20}$

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

Factor $4$ out of $20$ .

$- 6 \sqrt{3} + 3 \sqrt{3} + 3 \sqrt{4 (5)}$

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

$- 6 \sqrt{3} + 3 \sqrt{3} + 3 \sqrt{2^{2} \cdot 5}$

Pull terms out from under the radical.

$- 6 \sqrt{3} + 3 \sqrt{3} + 3 (| 2 | \sqrt{5})$

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

$- 6 \sqrt{3} + 3 \sqrt{3} + 3 (2 \sqrt{5})$

Multiply $2$ by $3$ .

$- 6 \sqrt{3} + 3 \sqrt{3} + 6 \sqrt{5}$

Step 2

Add $- 6 \sqrt{3}$ and $3 \sqrt{3}$ .

$- 3 \sqrt{3} + 6 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 3 \sqrt{3} + 6 \sqrt{5}$

Decimal Form:

$8.22025544 \dots$