Algebra Examples

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

Step 1

Multiply $3 \sqrt{x} (4 \sqrt{3 x})$ .

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Step 1.1

Multiply $4$ by $3$ .

$12 \sqrt{x} \sqrt{3 x} \cdot \sqrt{6 x}$

Step 1.2

Combine using the product rule for radicals.

$12 \sqrt{3 x \cdot x} \cdot \sqrt{6 x}$

Step 1.3

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

$12 \sqrt{3 (x^{1} x)} \cdot \sqrt{6 x}$

Step 1.4

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

$12 \sqrt{3 (x^{1} x^{1})} \cdot \sqrt{6 x}$

Step 1.5

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

$12 \sqrt{3 x^{1 + 1}} \cdot \sqrt{6 x}$

Step 1.6

Add $1$ and $1$ .

$12 \sqrt{3 x^{2}} \cdot \sqrt{6 x}$

$12 \sqrt{3 x^{2}} \cdot \sqrt{6 x}$

Step 2

Reorder $3$ and $x^{2}$ .

$12 \sqrt{x^{2} \cdot 3} \cdot \sqrt{6 x}$

Step 3

Pull terms out from under the radical.

$12 (x \sqrt{3}) \cdot \sqrt{6 x}$

Step 4

Multiply $12 x \sqrt{3} \sqrt{6 x}$ .

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Step 4.1

Combine using the product rule for radicals.

$12 x \sqrt{6 x \cdot 3}$

Step 4.2

Multiply $3$ by $6$ .

$12 x \sqrt{18 x}$

$12 x \sqrt{18 x}$

Step 5

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

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Step 5.1

Factor $9$ out of $18$ .

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

Step 5.2

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

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

Step 5.3

Add parentheses.

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

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

Step 6

Pull terms out from under the radical.

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

Step 7

Multiply $3$ by $12$ .

$36 x \sqrt{2 x}$

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