Simplify square root of 20x^3y* square root of 4xy^6

$\sqrt{20 x^{3} y} \cdot \sqrt{4 x y^{6}}$

Rewrite $20 x^{3} y$ as ${(2 x)}^{2} \cdot (5 x y)$ .

Factor $4$ out of $20$ .

$\sqrt{4 (5) x^{3} y} \cdot \sqrt{4 x y^{6}}$

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

$\sqrt{2^{2} \cdot 5 x^{3} y} \cdot \sqrt{4 x y^{6}}$

Factor out $x^{2}$ .

$\sqrt{2^{2} \cdot 5 (x^{2} x) y} \cdot \sqrt{4 x y^{6}}$

Move $5$ .

$\sqrt{2^{2} x^{2} \cdot 5 x y} \cdot \sqrt{4 x y^{6}}$

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

$\sqrt{{(2 x)}^{2} \cdot 5 x y} \cdot \sqrt{4 x y^{6}}$

Add parentheses.

$\sqrt{{(2 x)}^{2} \cdot 5 (x y)} \cdot \sqrt{4 x y^{6}}$

Add parentheses.

$\sqrt{{(2 x)}^{2} \cdot (5 x y)} \cdot \sqrt{4 x y^{6}}$

Pull terms out from under the radical.

$2 x \sqrt{5 x y} \cdot \sqrt{4 x y^{6}}$

Rewrite $4 x y^{6}$ as ${(2 y^{3})}^{2} x$ .

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

$2 x \sqrt{5 x y} \cdot \sqrt{2^{2} x y^{6}}$

Rewrite $y^{6}$ as ${(y^{3})}^{2}$ .

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

Move $x$ .

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

Rewrite $2^{2} {(y^{3})}^{2}$ as ${(2 y^{3})}^{2}$ .

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

Pull terms out from under the radical.

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

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

Multiply $2$ by $2$ .

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

Combine using the product rule for radicals.

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

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

$4 x (y^{3} \sqrt{5 (x^{1} x) y})$

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

$4 x (y^{3} \sqrt{5 (x^{1} x^{1}) y})$

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

$4 x (y^{3} \sqrt{5 x^{1 + 1} y})$

Add $1$ and $1$ .

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

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

Reorder $5$ and $x^{2}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$4 (x \cdot x) (y^{3} (\sqrt{5 y}))$

Multiply $x$ by $x$ .

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

$4 x^{2} y^{3} \sqrt{5 y}$

Simplify square root of 20x^3y* square root of 4xy^6

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