Simplify square root of 48+ square root of 24-3 square root of 12

$\sqrt{48} + \sqrt{24} - 3 \sqrt{12}$

Step 1

Simplify each term.

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

Factor $16$ out of $48$ .

$\sqrt{16 (3)} + \sqrt{24} - 3 \sqrt{12}$

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

$\sqrt{4^{2} \cdot 3} + \sqrt{24} - 3 \sqrt{12}$

Pull terms out from under the radical.

$4 \sqrt{3} + \sqrt{24} - 3 \sqrt{12}$

Rewrite $24$ as $2^{2} \cdot 6$ .

Factor $4$ out of $24$ .

$4 \sqrt{3} + \sqrt{4 (6)} - 3 \sqrt{12}$

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

$4 \sqrt{3} + \sqrt{2^{2} \cdot 6} - 3 \sqrt{12}$

Pull terms out from under the radical.

$4 \sqrt{3} + 2 \sqrt{6} - 3 \sqrt{12}$

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

Factor $4$ out of $12$ .

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

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

$4 \sqrt{3} + 2 \sqrt{6} - 3 \sqrt{2^{2} \cdot 3}$

Pull terms out from under the radical.

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

Multiply $2$ by $- 3$ .

$4 \sqrt{3} + 2 \sqrt{6} - 6 \sqrt{3}$

Step 2

Subtract $6 \sqrt{3}$ from $4 \sqrt{3}$ .

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$1.43487787 \dots$