Algebra Examples

$\sqrt{32 x y} \cdot \sqrt{4 x y^{2}}$

Step 1

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

Tap for more steps...

Step 1.1

Factor $16$ out of $32$ .

$\sqrt{16 (2) x y} \cdot \sqrt{4 x y^{2}}$

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Add parentheses.

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

Step 1.5

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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

Step 4

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

Tap for more steps...

Step 4.1

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

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

Step 4.2

Move $x$ .

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

Step 4.3

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

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

Step 5

Pull terms out from under the radical.

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

Step 6

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

Tap for more steps...

Step 6.1

Multiply $2$ by $4$ .

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

Step 6.2

Combine using the product rule for radicals.

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

Step 6.3

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

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

Step 6.4

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

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

Step 6.5

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

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

Step 6.6

Add $1$ and $1$ .

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

Step 7

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

Tap for more steps...

Step 7.1

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

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

Step 7.2

Add parentheses.

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

Step 8

Pull terms out from under the radical.

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

Step 9

Reorder factors in $8 y (x \sqrt{2 y})$ .

$8 y x \sqrt{2 y}$