Evaluate square root of 12-2 square root of 3+ square root of 108

$\sqrt{12} - 2 \sqrt{3} + \sqrt{108}$

Step 1

Simplify each term.

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

Factor $4$ out of $12$ .

$\sqrt{4 (3)} - 2 \sqrt{3} + \sqrt{108}$

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

$\sqrt{2^{2} \cdot 3} - 2 \sqrt{3} + \sqrt{108}$

$\sqrt{2^{2} \cdot 3} - 2 \sqrt{3} + \sqrt{108}$

Pull terms out from under the radical.

$2 \sqrt{3} - 2 \sqrt{3} + \sqrt{108}$

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

Factor $36$ out of $108$ .

$2 \sqrt{3} - 2 \sqrt{3} + \sqrt{36 (3)}$

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

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

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

Pull terms out from under the radical.

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

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

Step 2

Simplify by adding terms.

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

$0 + 6 \sqrt{3}$

Add $0$ and $6 \sqrt{3}$ .

$6 \sqrt{3}$

$6 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{3}$

Decimal Form:

$10.39230484 \dots$

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