Evaluate square root of 75-4 square root of 18+2 square root of 32

$\sqrt{75} - 4 \sqrt{18} + 2 \sqrt{32}$

Step 1

Simplify each term.

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

Factor $25$ out of $75$ .

$\sqrt{25 (3)} - 4 \sqrt{18} + 2 \sqrt{32}$

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

$\sqrt{5^{2} \cdot 3} - 4 \sqrt{18} + 2 \sqrt{32}$

Pull terms out from under the radical.

$5 \sqrt{3} - 4 \sqrt{18} + 2 \sqrt{32}$

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$5 \sqrt{3} - 4 \sqrt{9 (2)} + 2 \sqrt{32}$

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

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

Pull terms out from under the radical.

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

Multiply $3$ by $- 4$ .

$5 \sqrt{3} - 12 \sqrt{2} + 2 \sqrt{32}$

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

Factor $16$ out of $32$ .

$5 \sqrt{3} - 12 \sqrt{2} + 2 \sqrt{16 (2)}$

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

$5 \sqrt{3} - 12 \sqrt{2} + 2 \sqrt{4^{2} \cdot 2}$

Pull terms out from under the radical.

$5 \sqrt{3} - 12 \sqrt{2} + 2 (4 \sqrt{2})$

Multiply $4$ by $2$ .

$5 \sqrt{3} - 12 \sqrt{2} + 8 \sqrt{2}$

Step 2

Add $- 12 \sqrt{2}$ and $8 \sqrt{2}$ .

$5 \sqrt{3} - 4 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{3} - 4 \sqrt{2}$

Decimal Form:

$3.00339978 \dots$