Simplify 3 square root of 32+2 square root of 50

$3 \sqrt{32} + 2 \sqrt{50}$

Step 1

Simplify each term.

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

Factor $16$ out of $32$ .

$3 \sqrt{16 (2)} + 2 \sqrt{50}$

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

$3 \sqrt{4^{2} \cdot 2} + 2 \sqrt{50}$

$3 \sqrt{4^{2} \cdot 2} + 2 \sqrt{50}$

Pull terms out from under the radical.

$3 (4 \sqrt{2}) + 2 \sqrt{50}$

Multiply $4$ by $3$ .

$12 \sqrt{2} + 2 \sqrt{50}$

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

Factor $25$ out of $50$ .

$12 \sqrt{2} + 2 \sqrt{25 (2)}$

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

$12 \sqrt{2} + 2 \sqrt{5^{2} \cdot 2}$

$12 \sqrt{2} + 2 \sqrt{5^{2} \cdot 2}$

Pull terms out from under the radical.

$12 \sqrt{2} + 2 (5 \sqrt{2})$

Multiply $5$ by $2$ .

$12 \sqrt{2} + 10 \sqrt{2}$

$12 \sqrt{2} + 10 \sqrt{2}$

Step 2

Add $12 \sqrt{2}$ and $10 \sqrt{2}$ .

$22 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$22 \sqrt{2}$

Decimal Form:

$31.11269837 \dots$

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