Simplify the Radical Expression square root of 12+ square root of 27- square root of 3

$\sqrt{12} + \sqrt{27} - \sqrt{3}$

Step 1

Simplify each term.

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

Factor $4$ out of $12$ .

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

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

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

Pull terms out from under the radical.

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

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

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

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

Factor $9$ out of $27$ .

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

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

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

Pull terms out from under the radical.

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

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

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

Step 2

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

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

Step 3

Subtract $\sqrt{3}$ from $5 \sqrt{3}$ .

$4 \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{3}$

Decimal Form:

$6.92820323 \dots$