Simplify the Radical Expression -8 square root of 108+ square root of 12

$- 8 \sqrt{108} + \sqrt{12}$

Step 1

Simplify each term.

Rewrite $108$ as $6^{2} \cdot 3$ .

Factor $36$ out of $108$ .

$- 8 \sqrt{36 (3)} + \sqrt{12}$

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

$- 8 \sqrt{6^{2} \cdot 3} + \sqrt{12}$

Pull terms out from under the radical.

$- 8 (| 6 | \sqrt{3}) + \sqrt{12}$

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

$- 8 (6 \sqrt{3}) + \sqrt{12}$

Multiply $6$ by $- 8$ .

$- 48 \sqrt{3} + \sqrt{12}$

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

Factor $4$ out of $12$ .

$- 48 \sqrt{3} + \sqrt{4 (3)}$

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

$- 48 \sqrt{3} + \sqrt{2^{2} \cdot 3}$

Pull terms out from under the radical.

$- 48 \sqrt{3} + | 2 | \sqrt{3}$

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

$- 48 \sqrt{3} + 2 \sqrt{3}$

Step 2

Add $- 48 \sqrt{3}$ and $2 \sqrt{3}$ .

$- 46 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 46 \sqrt{3}$

Decimal Form:

$- 79.67433714 \dots$