Simplify 8x^2 square root of 50x^3y^5

$8 x^{2} \sqrt{50 x^{3} y^{5}}$

Rewrite $50 x^{3} y^{5}$ as ${(5 x y^{2})}^{2} \cdot (2 x y)$ .

Factor $25$ out of $50$ .

$8 x^{2} \sqrt{25 (2) x^{3} y^{5}}$

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

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

Factor out $x^{2}$ .

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

Factor out $y^{4}$ .

$8 x^{2} \sqrt{5^{2} \cdot 2 (x^{2} x) (y^{4} y)}$

Rewrite $y^{4}$ as ${(y^{2})}^{2}$ .

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

Move $x$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

$8 (x^{1} x^{2}) (5 y^{2} \sqrt{2 x y})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$8 x^{1 + 2} (5 y^{2} \sqrt{2 x y})$

Add $1$ and $2$ .

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

Multiply $5$ by $8$ .

$40 x^{3} (y^{2} \sqrt{2 x y})$

Reorder factors in $40 x^{3} (y^{2} \sqrt{2 x y})$ .

$40 x^{3} y^{2} \sqrt{2 x y}$