Algebra Examples

$\frac{\sqrt{6}}{2} \cdot \sqrt{3}$

Step 1

Multiply $\frac{\sqrt{6}}{2} \sqrt{3}$ .

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Step 1.1

Combine $\frac{\sqrt{6}}{2}$ and $\sqrt{3}$ .

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

Step 1.2

Combine using the product rule for radicals.

$\frac{\sqrt{6 \cdot 3}}{2}$

Step 1.3

Multiply $6$ by $3$ .

$\frac{\sqrt{18}}{2}$

$\frac{\sqrt{18}}{2}$

Step 2

Simplify the numerator.

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Step 2.1

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

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Step 2.1.1

Factor $9$ out of $18$ .

$\frac{\sqrt{9 (2)}}{2}$

Step 2.1.2

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

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

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

Step 2.2

Pull terms out from under the radical.

$\frac{3 \sqrt{2}}{2}$

$\frac{3 \sqrt{2}}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{3 \sqrt{2}}{2}$

Decimal Form:

$2.12132034 \dots$

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