Evaluate 3 square root of 27-2 square root of 18+ square root of 12

$3 \sqrt{27} - 2 \sqrt{18} + \sqrt{12}$

Step 1

Simplify each term.

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

Factor $9$ out of $27$ .

$3 \sqrt{9 (3)} - 2 \sqrt{18} + \sqrt{12}$

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

$3 \sqrt{3^{2} \cdot 3} - 2 \sqrt{18} + \sqrt{12}$

$3 \sqrt{3^{2} \cdot 3} - 2 \sqrt{18} + \sqrt{12}$

Pull terms out from under the radical.

$3 (3 \sqrt{3}) - 2 \sqrt{18} + \sqrt{12}$

Multiply $3$ by $3$ .

$9 \sqrt{3} - 2 \sqrt{18} + \sqrt{12}$

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

Factor $9$ out of $18$ .

$9 \sqrt{3} - 2 \sqrt{9 (2)} + \sqrt{12}$

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

$9 \sqrt{3} - 2 \sqrt{3^{2} \cdot 2} + \sqrt{12}$

$9 \sqrt{3} - 2 \sqrt{3^{2} \cdot 2} + \sqrt{12}$

Pull terms out from under the radical.

$9 \sqrt{3} - 2 (3 \sqrt{2}) + \sqrt{12}$

Multiply $3$ by $- 2$ .

$9 \sqrt{3} - 6 \sqrt{2} + \sqrt{12}$

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

Factor $4$ out of $12$ .

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

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

$9 \sqrt{3} - 6 \sqrt{2} + \sqrt{2^{2} \cdot 3}$

$9 \sqrt{3} - 6 \sqrt{2} + \sqrt{2^{2} \cdot 3}$

Pull terms out from under the radical.

$9 \sqrt{3} - 6 \sqrt{2} + 2 \sqrt{3}$

$9 \sqrt{3} - 6 \sqrt{2} + 2 \sqrt{3}$

Step 2

Add $9 \sqrt{3}$ and $2 \sqrt{3}$ .

$11 \sqrt{3} - 6 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$11 \sqrt{3} - 6 \sqrt{2}$

Decimal Form:

$10.56727750 \dots$

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