Simplify square root of 50x^2y+x square root of 8y+3x square root of 2y

$\sqrt{50 x^{2} y} + x \sqrt{8 y} + 3 x \sqrt{2 y}$

Simplify each term.

Rewrite $50 x^{2} y$ as ${(5 x)}^{2} \cdot (2 y)$ .

Factor $25$ out of $50$ .

$\sqrt{25 (2) x^{2} y} + x \sqrt{8 y} + 3 x \sqrt{2 y}$

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

$\sqrt{5^{2} \cdot 2 x^{2} y} + x \sqrt{8 y} + 3 x \sqrt{2 y}$

Move $2$ .

$\sqrt{5^{2} x^{2} \cdot 2 y} + x \sqrt{8 y} + 3 x \sqrt{2 y}$

Rewrite $5^{2} x^{2}$ as ${(5 x)}^{2}$ .

$\sqrt{{(5 x)}^{2} \cdot 2 y} + x \sqrt{8 y} + 3 x \sqrt{2 y}$

Add parentheses.

$\sqrt{{(5 x)}^{2} \cdot (2 y)} + x \sqrt{8 y} + 3 x \sqrt{2 y}$

Pull terms out from under the radical.

$5 x \sqrt{2 y} + x \sqrt{8 y} + 3 x \sqrt{2 y}$

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

Factor $4$ out of $8$ .

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

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

$5 x \sqrt{2 y} + x \sqrt{2^{2} \cdot 2 y} + 3 x \sqrt{2 y}$

Add parentheses.

$5 x \sqrt{2 y} + x \sqrt{2^{2} \cdot (2 y)} + 3 x \sqrt{2 y}$

Pull terms out from under the radical.

$5 x \sqrt{2 y} + x (2 \sqrt{2 y}) + 3 x \sqrt{2 y}$

Rewrite using the commutative property of multiplication.

$5 x \sqrt{2 y} + 2 x \sqrt{2 y} + 3 x \sqrt{2 y}$

Simplify by adding terms.

Add $5 x \sqrt{2 y}$ and $2 x \sqrt{2 y}$ .

$7 x \sqrt{2 y} + 3 x \sqrt{2 y}$

Add $7 x \sqrt{2 y}$ and $3 x \sqrt{2 y}$ .

$10 x \sqrt{2 y}$