Basic Math Examples

\sqrt{75} + \sqrt{27}

$\sqrt{75} + \sqrt{27}$

Step 1

Simplify each term.

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Step 1.1

Rewrite

75

$75$ as

5^{2} \cdot 3

$5^{2} \cdot 3$ .

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Step 1.1.1

Factor

25

$25$ out of

75

$75$ .

\sqrt{25 (3)} + \sqrt{27}

$\sqrt{25 (3)} + \sqrt{27}$

Step 1.1.2

Rewrite

25

$25$ as

5^{2}

$5^{2}$ .

\sqrt{5^{2} \cdot 3} + \sqrt{27}

$\sqrt{5^{2} \cdot 3} + \sqrt{27}$

\sqrt{5^{2} \cdot 3} + \sqrt{27}

$\sqrt{5^{2} \cdot 3} + \sqrt{27}$

Step 1.2

Pull terms out from under the radical.

5 \sqrt{3} + \sqrt{27}

$5 \sqrt{3} + \sqrt{27}$

Step 1.3

Rewrite

27

$27$ as

3^{2} \cdot 3

$3^{2} \cdot 3$ .

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Step 1.3.1

Factor

9

$9$ out of

27

$27$ .

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

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

Step 1.3.2

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

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

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

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

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

Step 1.4

Pull terms out from under the radical.

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

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

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

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

Step 2

Add

5 \sqrt{3}

$5 \sqrt{3}$ and

3 \sqrt{3}

$3 \sqrt{3}$ .

8 \sqrt{3}

$8 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

8 \sqrt{3}

$8 \sqrt{3}$

Decimal Form:

13.85640646 \dots

$13.85640646 \dots$

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

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