Algebra Examples

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

Step 1

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

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Step 1.1

Combine using the product rule for radicals.

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

Step 1.2

Multiply $6$ by $3$ .

$\sqrt{18 x y}$

$\sqrt{18 x y}$

Step 2

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

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Step 2.1

Factor $9$ out of $18$ .

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

Step 2.2

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

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

Step 2.3

Add parentheses.

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

Step 2.4

Add parentheses.

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

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

Step 3

Pull terms out from under the radical.

$3 \sqrt{2 x y}$

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