Algebra Examples

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

Step 1

Simplify terms.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Combine using the product rule for radicals.

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

Step 1.3

Combine using the product rule for radicals.

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

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

Step 2

Simplify each term.

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Step 2.1

Multiply $15$ by $5$ .

$\sqrt{75} + \sqrt{15 \cdot 3}$

Step 2.2

Rewrite $75$ as $5^{2} \cdot 3$ .

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Step 2.2.1

Factor $25$ out of $75$ .

$\sqrt{25 (3)} + \sqrt{15 \cdot 3}$

Step 2.2.2

Rewrite $25$ as $5^{2}$ .

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

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

Step 2.3

Pull terms out from under the radical.

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

Step 2.4

Multiply $15$ by $3$ .

$5 \sqrt{3} + \sqrt{45}$

Step 2.5

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

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Step 2.5.1

Factor $9$ out of $45$ .

$5 \sqrt{3} + \sqrt{9 (5)}$

Step 2.5.2

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

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

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

Step 2.6

Pull terms out from under the radical.

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

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$15.36845797 \dots$

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