Simplify square root of x^2y^5 square root of xy

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

Step 1

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

Factor out $y^{4}$ .

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

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

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

Combine using the product rule for radicals.

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

Step 4

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

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

Step 5

Pull terms out from under the radical.

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

Step 6

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

Move $y$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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