Algebra Examples

$\sqrt{3 x^{2}} \cdot \sqrt{18 x}$

Step 1

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

$\sqrt{x^{2} \cdot 3} \cdot \sqrt{18 x}$

Step 2

Pull terms out from under the radical.

$x \sqrt{3} \cdot \sqrt{18 x}$

Step 3

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

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Step 3.1

Factor $9$ out of $18$ .

$x \sqrt{3} \cdot \sqrt{9 (2) x}$

Step 3.2

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

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

Step 3.3

Add parentheses.

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

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

Step 4

Pull terms out from under the radical.

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

Step 5

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

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Step 5.1

Combine using the product rule for radicals.

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

Step 5.2

Multiply $3$ by $2$ .

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

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

Step 6

Rewrite using the commutative property of multiplication.

$3 x \sqrt{6 x}$

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