Algebra Examples

$\sqrt{2 x^{3} y} \sqrt{12 x y}$

Step 1

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

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Step 1.1

Factor out $x^{2}$ .

$\sqrt{2 (x^{2} x) y} \sqrt{12 x y}$

Step 1.2

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

$\sqrt{x^{2} \cdot 2 x y} \sqrt{12 x y}$

Step 1.3

Add parentheses.

$\sqrt{x^{2} \cdot 2 (x y)} \sqrt{12 x y}$

Step 1.4

Add parentheses.

$\sqrt{x^{2} \cdot (2 x y)} \sqrt{12 x y}$

Step 2

Pull terms out from under the radical.

$x \sqrt{2 x y} \sqrt{12 x y}$

Step 3

Rewrite $12 x y$ as $2^{2} \cdot (3 x y)$ .

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Step 3.1

Factor $4$ out of $12$ .

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

Step 3.2

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

$x \sqrt{2 x y} \sqrt{2^{2} \cdot 3 x y}$

Step 3.3

Add parentheses.

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

Step 3.4

Add parentheses.

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

Step 4

Pull terms out from under the radical.

$x \sqrt{2 x y} (2 \sqrt{3 x y})$

Step 5

Rewrite using the commutative property of multiplication.

$2 x \sqrt{2 x y} \sqrt{3 x y}$

Step 6

Multiply $2 x \sqrt{2 x y} \sqrt{3 x y}$ .

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Step 6.1

Combine using the product rule for radicals.

$2 x \sqrt{3 x y (2 x y)}$

Step 6.2

Multiply $2$ by $3$ .

$2 x \sqrt{6 x y (x y)}$

Step 6.3

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

$2 x \sqrt{6 (x^{1} x) y \cdot y}$

Step 6.4

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

$2 x \sqrt{6 (x^{1} x^{1}) y \cdot y}$

Step 6.5

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

$2 x \sqrt{6 x^{1 + 1} y \cdot y}$

Step 6.6

Add $1$ and $1$ .

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

Step 6.7

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

$2 x \sqrt{6 x^{2} (y^{1} y)}$

Step 6.8

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

$2 x \sqrt{6 x^{2} (y^{1} y^{1})}$

Step 6.9

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

$2 x \sqrt{6 x^{2} y^{1 + 1}}$

Step 6.10

Add $1$ and $1$ .

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

Step 7

Rewrite $6 x^{2} y^{2}$ as ${(x y)}^{2} \cdot 6$ .

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Step 7.1

Move $6$ .

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

Step 7.2

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

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

Step 8

Pull terms out from under the radical.

$2 x (x y \sqrt{6})$

Step 9

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

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Step 9.1

Move $x$ .

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

Step 9.2

Multiply $x$ by $x$ .

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

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