Evaluate -2 square root of 48+3 square root of 75

$- 2 \sqrt{48} + 3 \sqrt{75}$

Step 1

Simplify each term.

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

Factor $16$ out of $48$ .

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

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

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

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

Pull terms out from under the radical.

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

Multiply $4$ by $- 2$ .

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

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

Factor $25$ out of $75$ .

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

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

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

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

Pull terms out from under the radical.

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

Multiply $5$ by $3$ .

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

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

Step 2

Add $- 8 \sqrt{3}$ and $15 \sqrt{3}$ .

$7 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$7 \sqrt{3}$

Decimal Form:

$12.12435565 \dots$

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