Evaluate 3 square root of 2+ square root of 50-4 square root of 8

$3 \sqrt{2} + \sqrt{50} - 4 \sqrt{8}$

Step 1

Simplify each term.

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$3 \sqrt{2} + \sqrt{25 (2)} - 4 \sqrt{8}$

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

$3 \sqrt{2} + \sqrt{5^{2} \cdot 2} - 4 \sqrt{8}$

Pull terms out from under the radical.

$3 \sqrt{2} + 5 \sqrt{2} - 4 \sqrt{8}$

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

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

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 4$ .

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

Step 2

Simplify by adding terms.

Add $3 \sqrt{2}$ and $5 \sqrt{2}$ .

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

Subtract $8 \sqrt{2}$ from $8 \sqrt{2}$ .

$0$