Algebra Examples

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

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

Step 1

Simplify terms.

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Step 1.1

Apply the distributive property.

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

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

Step 1.2

Combine using the product rule for radicals.

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

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

Step 1.3

Combine using the product rule for radicals.

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

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

\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

$15$ by

5

$5$ .

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

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

Step 2.2

Rewrite

75

$75$ as

5^{2} \cdot 3

$5^{2} \cdot 3$ .

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Step 2.2.1

Factor

25

$25$ out of

75

$75$ .

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

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

Step 2.2.2

Rewrite

25

$25$ as

5^{2}

$5^{2}$ .

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

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

\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}

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

Step 2.4

Multiply

15

$15$ by

3

$3$ .

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

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

Step 2.5

Rewrite

45

$45$ as

3^{2} \cdot 5

$3^{2} \cdot 5$ .

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Step 2.5.1

Factor

9

$9$ out of

45

$45$ .

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

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

Step 2.5.2

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

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

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

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}

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

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}

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

Decimal Form:

15.36845797 \dots

$15.36845797 \dots$

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

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