Algebra Examples

$2 \sqrt{x} \cdot 5 \sqrt{6 x} \cdot \sqrt{2 x}$

Step 1

Multiply $2 \sqrt{x} (5 \sqrt{6 x})$ .

Tap for more steps...

Step 1.1

Multiply $5$ by $2$ .

$10 \sqrt{x} \sqrt{6 x} \cdot \sqrt{2 x}$

Step 1.2

Combine using the product rule for radicals.

$10 \sqrt{6 x \cdot x} \cdot \sqrt{2 x}$

Step 1.3

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

$10 \sqrt{6 (x^{1} x)} \cdot \sqrt{2 x}$

Step 1.4

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

$10 \sqrt{6 (x^{1} x^{1})} \cdot \sqrt{2 x}$

Step 1.5

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

$10 \sqrt{6 x^{1 + 1}} \cdot \sqrt{2 x}$

Step 1.6

Add $1$ and $1$ .

$10 \sqrt{6 x^{2}} \cdot \sqrt{2 x}$

$10 \sqrt{6 x^{2}} \cdot \sqrt{2 x}$

Step 2

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

$10 \sqrt{x^{2} \cdot 6} \cdot \sqrt{2 x}$

Step 3

Pull terms out from under the radical.

$10 (x \sqrt{6}) \cdot \sqrt{2 x}$

Step 4

Multiply $10 x \sqrt{6} \sqrt{2 x}$ .

Tap for more steps...

Step 4.1

Combine using the product rule for radicals.

$10 x \sqrt{2 x \cdot 6}$

Step 4.2

Multiply $6$ by $2$ .

$10 x \sqrt{12 x}$

$10 x \sqrt{12 x}$

Step 5

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

Tap for more steps...

Step 5.1

Factor $4$ out of $12$ .

$10 x \sqrt{4 (3) x}$

Step 5.2

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

$10 x \sqrt{2^{2} \cdot 3 x}$

Step 5.3

Add parentheses.

$10 x \sqrt{2^{2} \cdot (3 x)}$

$10 x \sqrt{2^{2} \cdot (3 x)}$

Step 6

Pull terms out from under the radical.

$10 x (2 \sqrt{3 x})$

Step 7

Multiply $2$ by $10$ .

$20 x \sqrt{3 x}$

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