Basic Math Examples

\sqrt{72} + \sqrt{50}

$\sqrt{72} + \sqrt{50}$

Step 1

Simplify each term.

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Step 1.1

Rewrite

72

$72$ as

6^{2} \cdot 2

$6^{2} \cdot 2$ .

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Step 1.1.1

Factor

36

$36$ out of

72

$72$ .

\sqrt{36 (2)} + \sqrt{50}

$\sqrt{36 (2)} + \sqrt{50}$

Step 1.1.2

Rewrite

36

$36$ as

6^{2}

$6^{2}$ .

\sqrt{6^{2} \cdot 2} + \sqrt{50}

$\sqrt{6^{2} \cdot 2} + \sqrt{50}$

\sqrt{6^{2} \cdot 2} + \sqrt{50}

$\sqrt{6^{2} \cdot 2} + \sqrt{50}$

Step 1.2

Pull terms out from under the radical.

6 \sqrt{2} + \sqrt{50}

$6 \sqrt{2} + \sqrt{50}$

Step 1.3

Rewrite

50

$50$ as

5^{2} \cdot 2

$5^{2} \cdot 2$ .

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Step 1.3.1

Factor

25

$25$ out of

50

$50$ .

6 \sqrt{2} + \sqrt{25 (2)}

$6 \sqrt{2} + \sqrt{25 (2)}$

Step 1.3.2

Rewrite

25

$25$ as

5^{2}

$5^{2}$ .

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

$6 \sqrt{2} + \sqrt{5^{2} \cdot 2}$

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

$6 \sqrt{2} + \sqrt{5^{2} \cdot 2}$

Step 1.4

Pull terms out from under the radical.

6 \sqrt{2} + 5 \sqrt{2}

$6 \sqrt{2} + 5 \sqrt{2}$

6 \sqrt{2} + 5 \sqrt{2}

$6 \sqrt{2} + 5 \sqrt{2}$

Step 2

Add

6 \sqrt{2}

$6 \sqrt{2}$ and

5 \sqrt{2}

$5 \sqrt{2}$ .

11 \sqrt{2}

$11 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

11 \sqrt{2}

$11 \sqrt{2}$

Decimal Form:

15.55634918 \dots

$15.55634918 \dots$

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

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