Evaluate 2 square root of 48- square root of 75- square root of 12

$2 \sqrt{48} - \sqrt{75} - \sqrt{12}$

Step 1

Simplify each term.

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

Factor $16$ out of $48$ .

$2 \sqrt{16 (3)} - \sqrt{75} - \sqrt{12}$

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

$2 \sqrt{4^{2} \cdot 3} - \sqrt{75} - \sqrt{12}$

$2 \sqrt{4^{2} \cdot 3} - \sqrt{75} - \sqrt{12}$

Pull terms out from under the radical.

$2 (4 \sqrt{3}) - \sqrt{75} - \sqrt{12}$

Multiply $4$ by $2$ .

$8 \sqrt{3} - \sqrt{75} - \sqrt{12}$

Rewrite $75$ as $5^{2} \cdot 3$ .

Factor $25$ out of $75$ .

$8 \sqrt{3} - \sqrt{25 (3)} - \sqrt{12}$

Rewrite $25$ as $5^{2}$ .

$8 \sqrt{3} - \sqrt{5^{2} \cdot 3} - \sqrt{12}$

$8 \sqrt{3} - \sqrt{5^{2} \cdot 3} - \sqrt{12}$

Pull terms out from under the radical.

$8 \sqrt{3} - (5 \sqrt{3}) - \sqrt{12}$

Multiply $5$ by $- 1$ .

$8 \sqrt{3} - 5 \sqrt{3} - \sqrt{12}$

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

Factor $4$ out of $12$ .

$8 \sqrt{3} - 5 \sqrt{3} - \sqrt{4 (3)}$

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

$8 \sqrt{3} - 5 \sqrt{3} - \sqrt{2^{2} \cdot 3}$

$8 \sqrt{3} - 5 \sqrt{3} - \sqrt{2^{2} \cdot 3}$

Pull terms out from under the radical.

$8 \sqrt{3} - 5 \sqrt{3} - (2 \sqrt{3})$

Multiply $2$ by $- 1$ .

$8 \sqrt{3} - 5 \sqrt{3} - 2 \sqrt{3}$

$8 \sqrt{3} - 5 \sqrt{3} - 2 \sqrt{3}$

Step 2

Simplify by adding terms.

Subtract $5 \sqrt{3}$ from $8 \sqrt{3}$ .

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

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

$\sqrt{3}$

$\sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{3}$

Decimal Form:

$1.73205080 \dots$

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