Basic Math Examples

$\sqrt{39} \cdot \sqrt{3} + 10 \sqrt{13}$

Step 1

Simplify each term.

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Step 1.1

Combine using the product rule for radicals.

$\sqrt{39 \cdot 3} + 10 \sqrt{13}$

Step 1.2

Multiply $39$ by $3$ .

$\sqrt{117} + 10 \sqrt{13}$

Step 1.3

Rewrite $117$ as $3^{2} \cdot 13$ .

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Step 1.3.1

Factor $9$ out of $117$ .

$\sqrt{9 (13)} + 10 \sqrt{13}$

Step 1.3.2

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

$\sqrt{3^{2} \cdot 13} + 10 \sqrt{13}$

$\sqrt{3^{2} \cdot 13} + 10 \sqrt{13}$

Step 1.4

Pull terms out from under the radical.

$3 \sqrt{13} + 10 \sqrt{13}$

$3 \sqrt{13} + 10 \sqrt{13}$

Step 2

Add $3 \sqrt{13}$ and $10 \sqrt{13}$ .

$13 \sqrt{13}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$13 \sqrt{13}$

Decimal Form:

$46.87216658 \dots$

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