Algebra Examples

$\sqrt{4 x y^{3}} \cdot \sqrt{6 y}$

Step 1

Rewrite $4 x y^{3}$ as ${(2 y)}^{2} (x y)$ .

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Step 1.1

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

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

Step 1.2

Factor out $y^{2}$ .

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

Step 1.3

Move $x$ .

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

Step 1.4

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

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

Step 1.5

Add parentheses.

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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Step 3.1

Combine using the product rule for radicals.

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

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

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

Step 3.5

Add $1$ and $1$ .

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

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

Step 4

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

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Step 4.1

Move $x$ .

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

Step 4.2

Reorder $6$ and $y^{2}$ .

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

Step 4.3

Add parentheses.

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

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

Step 5

Pull terms out from under the radical.

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

Step 6

Multiply $y$ by $y$ by adding the exponents.

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Step 6.1

Move $y$ .

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

Step 6.2

Multiply $y$ by $y$ .

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

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$