Algebra Examples

$\sqrt{2 x^{3} y} \cdot \sqrt{6 x^{2} y^{2}}$

Step 1

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

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Step 1.1

Factor out $x^{2}$ .

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

Step 1.2

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

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

Step 1.3

Add parentheses.

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

Step 1.4

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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Step 3.1

Move $6$ .

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

Step 3.2

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

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

Step 4

Pull terms out from under the radical.

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

Step 5

Rewrite using the commutative property of multiplication.

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

Step 6

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

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Step 6.1

Move $x$ .

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

Step 6.2

Multiply $x$ by $x$ .

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

Step 7

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

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Step 7.1

Combine using the product rule for radicals.

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

Step 7.2

Multiply $6$ by $2$ .

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

Step 8

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

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Step 8.1

Factor $4$ out of $12$ .

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

Step 8.2

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

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

Step 8.3

Add parentheses.

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

Step 8.4

Add parentheses.

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

Step 9

Pull terms out from under the radical.

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

Step 10

Rewrite using the commutative property of multiplication.

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