Simplify square root of 8mn^2+2n square root of 18m

$\sqrt{8 m n^{2}} + 2 n \sqrt{18 m}$

Step 1

Simplify each term.

Rewrite $8 m n^{2}$ as ${(2 n)}^{2} \cdot (2 m)$ .

Factor $4$ out of $8$ .

$\sqrt{4 (2) m n^{2}} + 2 n \sqrt{18 m}$

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

$\sqrt{2^{2} \cdot 2 m n^{2}} + 2 n \sqrt{18 m}$

Move $m$ .

$\sqrt{2^{2} \cdot 2 n^{2} m} + 2 n \sqrt{18 m}$

Move $2$ .

$\sqrt{2^{2} n^{2} \cdot 2 m} + 2 n \sqrt{18 m}$

Rewrite $2^{2} n^{2}$ as ${(2 n)}^{2}$ .

$\sqrt{{(2 n)}^{2} \cdot 2 m} + 2 n \sqrt{18 m}$

Add parentheses.

$\sqrt{{(2 n)}^{2} \cdot (2 m)} + 2 n \sqrt{18 m}$

Pull terms out from under the radical.

$2 n \sqrt{2 m} + 2 n \sqrt{18 m}$

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

Factor $9$ out of $18$ .

$2 n \sqrt{2 m} + 2 n \sqrt{9 (2) m}$

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

$2 n \sqrt{2 m} + 2 n \sqrt{3^{2} \cdot 2 m}$

Add parentheses.

$2 n \sqrt{2 m} + 2 n \sqrt{3^{2} \cdot (2 m)}$

Pull terms out from under the radical.

$2 n \sqrt{2 m} + 2 n (3 \sqrt{2 m})$

Multiply $3$ by $2$ .

$2 n \sqrt{2 m} + 6 n \sqrt{2 m}$

Step 2

Add $2 n \sqrt{2 m}$ and $6 n \sqrt{2 m}$ .

$8 n \sqrt{2 m}$