Algebra Examples

$\frac{1}{3} \sqrt{15} \cdot \sqrt{6}$

Step 1

Combine $\frac{1}{3}$ and $\sqrt{15}$ .

$\frac{\sqrt{15}}{3} \cdot \sqrt{6}$

Step 2

Multiply $\frac{\sqrt{15}}{3} \sqrt{6}$ .

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Step 2.1

Combine $\frac{\sqrt{15}}{3}$ and $\sqrt{6}$ .

$\frac{\sqrt{15} \sqrt{6}}{3}$

Step 2.2

Combine using the product rule for radicals.

$\frac{\sqrt{15 \cdot 6}}{3}$

Step 2.3

Multiply $15$ by $6$ .

$\frac{\sqrt{90}}{3}$

$\frac{\sqrt{90}}{3}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $90$ as $3^{2} \cdot 10$ .

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Step 3.1.1

Factor $9$ out of $90$ .

$\frac{\sqrt{9 (10)}}{3}$

Step 3.1.2

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

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

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

Step 3.2

Pull terms out from under the radical.

$\frac{3 \sqrt{10}}{3}$

$\frac{3 \sqrt{10}}{3}$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Cancel the common factor.

$\frac{3 \sqrt{10}}{3}$

Step 4.2

Divide $\sqrt{10}$ by $1$ .

$\sqrt{10}$

$\sqrt{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt{10}$

Decimal Form:

$3.16227766 \dots$

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