Algebra Examples

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

Step 1

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

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Step 1.1

Combine using the product rule for radicals.

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

Step 1.2

Multiply $6$ by $2$ .

$\sqrt{12 x \cdot x}$

Step 1.3

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

$\sqrt{12 (x^{1} x)}$

Step 1.4

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

$\sqrt{12 (x^{1} x^{1})}$

Step 1.5

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

$\sqrt{12 x^{1 + 1}}$

Step 1.6

Add $1$ and $1$ .

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

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

Step 2

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

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Step 2.1

Factor $4$ out of $12$ .

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

Step 2.2

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

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

Step 2.3

Move $3$ .

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

Step 2.4

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

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

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

Step 3

Pull terms out from under the radical.

$2 x \sqrt{3}$

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