Pre-Algebra Examples

$\sqrt{15} (5 + \sqrt{3})$

Step 1

Simplify terms.

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Step 1.1

Apply the distributive property.

$\sqrt{15} \cdot 5 + \sqrt{15} \sqrt{3}$

Step 1.2

Move $5$ to the left of $\sqrt{15}$ .

$5 \cdot \sqrt{15} + \sqrt{15} \sqrt{3}$

Step 1.3

Combine using the product rule for radicals.

$5 \cdot \sqrt{15} + \sqrt{15 \cdot 3}$

$5 \cdot \sqrt{15} + \sqrt{15 \cdot 3}$

Step 2

Simplify each term.

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Step 2.1

Multiply $15$ by $3$ .

$5 \sqrt{15} + \sqrt{45}$

Step 2.2

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

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Step 2.2.1

Factor $9$ out of $45$ .

$5 \sqrt{15} + \sqrt{9 (5)}$

Step 2.2.2

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

$5 \sqrt{15} + \sqrt{3^{2} \cdot 5}$

$5 \sqrt{15} + \sqrt{3^{2} \cdot 5}$

Step 2.3

Pull terms out from under the radical.

$5 \sqrt{15} + 3 \sqrt{5}$

$5 \sqrt{15} + 3 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{15} + 3 \sqrt{5}$

Decimal Form:

$26.07312066 \dots$

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