Simplify square root of 2xy^2* square root of 32xy

$\sqrt{2 x y^{2}} \cdot \sqrt{32 x y}$

Step 1

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

Move $x$ .

$\sqrt{2 y^{2} x} \cdot \sqrt{32 x y}$

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

$\sqrt{y^{2} \cdot 2 x} \cdot \sqrt{32 x y}$

Add parentheses.

$\sqrt{y^{2} \cdot (2 x)} \cdot \sqrt{32 x y}$

Step 2

Pull terms out from under the radical.

$y \sqrt{2 x} \cdot \sqrt{32 x y}$

Step 3

Rewrite $32 x y$ as ${(2^{2})}^{2} \cdot (2 x y)$ .

Factor $16$ out of $32$ .

$y \sqrt{2 x} \cdot \sqrt{16 (2) x y}$

Rewrite $16$ as $4^{2}$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Step 4

Pull terms out from under the radical.

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

Step 5

Simplify the expression.

Rewrite using the commutative property of multiplication.

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

Raise $2$ to the power of $2$ .

$4 y \sqrt{2 x} \sqrt{2 x y}$

Step 6

Multiply $4 y \sqrt{2 x} \sqrt{2 x y}$ .

Combine using the product rule for radicals.

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

Multiply $2$ by $2$ .

$4 y \sqrt{4 x y x}$

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

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

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

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

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

$4 y \sqrt{4 x^{1 + 1} y}$

Add $1$ and $1$ .

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

Step 7

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

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

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

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

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

Step 8

Pull terms out from under the radical.

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

Step 9

Simplify the expression.

Multiply $2$ by $4$ .

$8 y (x \sqrt{y})$

Reorder factors in $8 y (x \sqrt{y})$ .

$8 y x \sqrt{y}$

Simplify square root of 2xy^2* square root of 32xy

Related Questions

Support LCMGCF.com by disabling your adblocker.