Evaluate square root of 27- square root of 12

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

Step 1

Simplify each term.

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

Factor $9$ out of $27$ .

$\sqrt{9 (3)} - \sqrt{12}$

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

$\sqrt{3^{2} \cdot 3} - \sqrt{12}$

$\sqrt{3^{2} \cdot 3} - \sqrt{12}$

Pull terms out from under the radical.

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

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

Factor $4$ out of $12$ .

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

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

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 1$ .

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

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

Step 2

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

$\sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{3}$

Decimal Form:

$1.73205080 \dots$

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