Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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Step 3.1

Factor $16$ out of $32$ .

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

Add parentheses.

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

Step 3.5

Add parentheses.

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

Step 4

Pull terms out from under the radical.

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

Step 5

Simplify the expression.

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Step 5.1

Rewrite using the commutative property of multiplication.

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

Step 5.2

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

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

Step 6

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

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Step 6.1

Combine using the product rule for radicals.

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

Step 6.2

Multiply $2$ by $2$ .

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

Step 6.3

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

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

Step 6.4

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

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

Step 6.5

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

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

Step 6.6

Add $1$ and $1$ .

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

Step 7

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

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Step 7.1

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

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

Step 7.2

Move $x$ .

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

Step 7.3

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

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

Step 8

Pull terms out from under the radical.

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

Step 9

Multiply $2$ by $4$ .

$8 x y \sqrt{x}$