Evaluate 5 square root of 48-2 square root of 32+ square root of 75

$5 \sqrt{48} - 2 \sqrt{32} + \sqrt{75}$

Simplify each term.

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

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Factor $16$ out of $48$ .

$5 \sqrt{16 (3)} - 2 \sqrt{32} + \sqrt{75}$

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

$5 \sqrt{4^{2} \cdot 3} - 2 \sqrt{32} + \sqrt{75}$

Pull terms out from under the radical.

$5 (4 \sqrt{3}) - 2 \sqrt{32} + \sqrt{75}$

Multiply $4$ by $5$ .

$20 \sqrt{3} - 2 \sqrt{32} + \sqrt{75}$

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

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Factor $16$ out of $32$ .

$20 \sqrt{3} - 2 \sqrt{16 (2)} + \sqrt{75}$

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

$20 \sqrt{3} - 2 \sqrt{4^{2} \cdot 2} + \sqrt{75}$

Pull terms out from under the radical.

$20 \sqrt{3} - 2 (4 \sqrt{2}) + \sqrt{75}$

Multiply $4$ by $- 2$ .

$20 \sqrt{3} - 8 \sqrt{2} + \sqrt{75}$

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

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Factor $25$ out of $75$ .

$20 \sqrt{3} - 8 \sqrt{2} + \sqrt{25 (3)}$

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

$20 \sqrt{3} - 8 \sqrt{2} + \sqrt{5^{2} \cdot 3}$

Pull terms out from under the radical.

$20 \sqrt{3} - 8 \sqrt{2} + 5 \sqrt{3}$

Add $20 \sqrt{3}$ and $5 \sqrt{3}$ .

$25 \sqrt{3} - 8 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$25 \sqrt{3} - 8 \sqrt{2}$

Decimal Form:

$31.98756169 \dots$

Evaluate 5 square root of 48-2 square root of 32+ square root of 75

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