Precalculus Examples

$\sqrt{3} \sqrt{15}$

Step 1

Combine using the product rule for radicals.

$\sqrt{3 \cdot 15}$

Step 2

Multiply $3$ by $15$ .

$\sqrt{45}$

Step 3

Rewrite $45$ as $3^{2} \cdot 5$ .

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Step 3.1

Factor $9$ out of $45$ .

$\sqrt{9 (5)}$

Step 3.2

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

$\sqrt{3^{2} \cdot 5}$

$\sqrt{3^{2} \cdot 5}$

Step 4

Pull terms out from under the radical.

$3 \sqrt{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{5}$

Decimal Form:

$6.70820393 \dots$

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