Simplify square root of 20xy^2* square root of 5xy

$\sqrt{20 x y^{2}} \cdot \sqrt{5 x y}$

Step 1

Rewrite $20 x y^{2}$ as ${(2 y)}^{2} \cdot (5 x)$ .

Factor $4$ out of $20$ .

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

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

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

Move $x$ .

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

Move $5$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$2 y \sqrt{5 x} \cdot \sqrt{5 x y}$

Step 3

Multiply $2 y \sqrt{5 x} \sqrt{5 x y}$ .

Combine using the product rule for radicals.

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

Multiply $5$ by $5$ .

$2 y \sqrt{25 x y x}$

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

$2 y \sqrt{25 (x^{1} x) y}$

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

$2 y \sqrt{25 (x^{1} x^{1}) y}$

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

$2 y \sqrt{25 x^{1 + 1} y}$

Add $1$ and $1$ .

$2 y \sqrt{25 x^{2} y}$

Step 4

Rewrite $25 x^{2} y$ as ${(5 x)}^{2} y$ .

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

$2 y \sqrt{5^{2} x^{2} y}$

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

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

Step 5

Pull terms out from under the radical.

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

Step 6

Simplify the expression.

Multiply $5$ by $2$ .

$10 y (x \sqrt{y})$

Reorder factors in $10 y (x \sqrt{y})$ .

$10 y x \sqrt{y}$

Simplify square root of 20xy^2* square root of 5xy

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