Evaluate 3 square root of 48-2 square root of 32+ square root of 27

$3 \sqrt{48} - 2 \sqrt{32} + \sqrt{27}$

Step 1

Simplify each term.

Rewrite $48$ as $4^{2} \cdot 3$ .

Factor $16$ out of $48$ .

$3 \sqrt{16 (3)} - 2 \sqrt{32} + \sqrt{27}$

Rewrite $16$ as $4^{2}$ .

$3 \sqrt{4^{2} \cdot 3} - 2 \sqrt{32} + \sqrt{27}$

Pull terms out from under the radical.

$3 (4 \sqrt{3}) - 2 \sqrt{32} + \sqrt{27}$

Multiply $4$ by $3$ .

$12 \sqrt{3} - 2 \sqrt{32} + \sqrt{27}$

Rewrite $32$ as $4^{2} \cdot 2$ .

Factor $16$ out of $32$ .

$12 \sqrt{3} - 2 \sqrt{16 (2)} + \sqrt{27}$

Rewrite $16$ as $4^{2}$ .

$12 \sqrt{3} - 2 \sqrt{4^{2} \cdot 2} + \sqrt{27}$

Pull terms out from under the radical.

$12 \sqrt{3} - 2 (4 \sqrt{2}) + \sqrt{27}$

Multiply $4$ by $- 2$ .

$12 \sqrt{3} - 8 \sqrt{2} + \sqrt{27}$

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

Factor $9$ out of $27$ .

$12 \sqrt{3} - 8 \sqrt{2} + \sqrt{9 (3)}$

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

$12 \sqrt{3} - 8 \sqrt{2} + \sqrt{3^{2} \cdot 3}$

Pull terms out from under the radical.

$12 \sqrt{3} - 8 \sqrt{2} + 3 \sqrt{3}$

Step 2

Add $12 \sqrt{3}$ and $3 \sqrt{3}$ .

$15 \sqrt{3} - 8 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$15 \sqrt{3} - 8 \sqrt{2}$

Decimal Form:

$14.66705361 \dots$