Trigonometry Examples

$\sqrt{18 x} \cdot \sqrt{12 x}$

Step 1

Rewrite $18 x$ as $3^{2} \cdot (2 x)$ .

Tap for more steps...

Step 1.1

Factor $9$ out of $18$ .

$\sqrt{9 (2) x} \cdot \sqrt{12 x}$

Step 1.2

Rewrite $9$ as $3^{2}$ .

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

Step 1.3

Add parentheses.

$\sqrt{3^{2} \cdot (2 x)} \cdot \sqrt{12 x}$

$\sqrt{3^{2} \cdot (2 x)} \cdot \sqrt{12 x}$

Step 2

Pull terms out from under the radical.

$3 \sqrt{2 x} \cdot \sqrt{12 x}$

Step 3

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

Tap for more steps...

Step 3.1

Factor $4$ out of $12$ .

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

Step 3.2

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

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

Step 3.3

Add parentheses.

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

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

Step 4

Pull terms out from under the radical.

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

Step 5

Multiply $3 \sqrt{2 x} (2 \sqrt{3 x})$ .

Tap for more steps...

Step 5.1

Multiply $2$ by $3$ .

$6 \sqrt{2 x} \sqrt{3 x}$

Step 5.2

Combine using the product rule for radicals.

$6 \sqrt{3 x (2 x)}$

Step 5.3

Multiply $2$ by $3$ .

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

Step 5.4

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

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

Step 5.5

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

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

Step 5.6

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

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

Step 5.7

Add $1$ and $1$ .

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

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

Step 6

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

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

Step 7

Pull terms out from under the radical.

$6 x \sqrt{6}$

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