Simplify the Radical Expression square root of 12+2 square root of 18-4 square root of 27

$\sqrt{12} + 2 \sqrt{18} - 4 \sqrt{27}$

Step 1

Simplify each term.

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

Factor $4$ out of $12$ .

$\sqrt{4 (3)} + 2 \sqrt{18} - 4 \sqrt{27}$

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

$\sqrt{2^{2} \cdot 3} + 2 \sqrt{18} - 4 \sqrt{27}$

Pull terms out from under the radical.

$| 2 | \sqrt{3} + 2 \sqrt{18} - 4 \sqrt{27}$

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

$2 \sqrt{3} + 2 \sqrt{18} - 4 \sqrt{27}$

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$2 \sqrt{3} + 2 \sqrt{9 (2)} - 4 \sqrt{27}$

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

$2 \sqrt{3} + 2 \sqrt{3^{2} \cdot 2} - 4 \sqrt{27}$

Pull terms out from under the radical.

$2 \sqrt{3} + 2 (| 3 | \sqrt{2}) - 4 \sqrt{27}$

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

$2 \sqrt{3} + 2 (3 \sqrt{2}) - 4 \sqrt{27}$

Multiply $3$ by $2$ .

$2 \sqrt{3} + 6 \sqrt{2} - 4 \sqrt{27}$

Rewrite $27$ as $3^{2} \cdot 3$ .

Factor $9$ out of $27$ .

$2 \sqrt{3} + 6 \sqrt{2} - 4 \sqrt{9 (3)}$

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

$2 \sqrt{3} + 6 \sqrt{2} - 4 \sqrt{3^{2} \cdot 3}$

Pull terms out from under the radical.

$2 \sqrt{3} + 6 \sqrt{2} - 4 (| 3 | \sqrt{3})$

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

$2 \sqrt{3} + 6 \sqrt{2} - 4 (3 \sqrt{3})$

Multiply $3$ by $- 4$ .

$2 \sqrt{3} + 6 \sqrt{2} - 12 \sqrt{3}$

Step 2

Subtract $12 \sqrt{3}$ from $2 \sqrt{3}$ .

$- 10 \sqrt{3} + 6 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 10 \sqrt{3} + 6 \sqrt{2}$

Decimal Form:

$- 8.83522670 \dots$