Basic Math Examples

3 \sqrt{175} + \sqrt{112}

$3 \sqrt{175} + \sqrt{112}$

Step 1

Simplify each term.

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Step 1.1

Rewrite

175

$175$ as

5^{2} \cdot 7

$5^{2} \cdot 7$ .

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Step 1.1.1

Factor

25

$25$ out of

175

$175$ .

3 \sqrt{25 (7)} + \sqrt{112}

$3 \sqrt{25 (7)} + \sqrt{112}$

Step 1.1.2

Rewrite

25

$25$ as

5^{2}

$5^{2}$ .

3 \sqrt{5^{2} \cdot 7} + \sqrt{112}

$3 \sqrt{5^{2} \cdot 7} + \sqrt{112}$

3 \sqrt{5^{2} \cdot 7} + \sqrt{112}

$3 \sqrt{5^{2} \cdot 7} + \sqrt{112}$

Step 1.2

Pull terms out from under the radical.

3 (5 \sqrt{7}) + \sqrt{112}

$3 (5 \sqrt{7}) + \sqrt{112}$

Step 1.3

Multiply

5

$5$ by

3

$3$ .

15 \sqrt{7} + \sqrt{112}

$15 \sqrt{7} + \sqrt{112}$

Step 1.4

Rewrite

112

$112$ as

4^{2} \cdot 7

$4^{2} \cdot 7$ .

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Step 1.4.1

Factor

16

$16$ out of

112

$112$ .

15 \sqrt{7} + \sqrt{16 (7)}

$15 \sqrt{7} + \sqrt{16 (7)}$

Step 1.4.2

Rewrite

16

$16$ as

4^{2}

$4^{2}$ .

15 \sqrt{7} + \sqrt{4^{2} \cdot 7}

$15 \sqrt{7} + \sqrt{4^{2} \cdot 7}$

15 \sqrt{7} + \sqrt{4^{2} \cdot 7}

$15 \sqrt{7} + \sqrt{4^{2} \cdot 7}$

Step 1.5

Pull terms out from under the radical.

15 \sqrt{7} + 4 \sqrt{7}

$15 \sqrt{7} + 4 \sqrt{7}$

15 \sqrt{7} + 4 \sqrt{7}

$15 \sqrt{7} + 4 \sqrt{7}$

Step 2

Add

15 \sqrt{7}

$15 \sqrt{7}$ and

4 \sqrt{7}

$4 \sqrt{7}$ .

19 \sqrt{7}

$19 \sqrt{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

19 \sqrt{7}

$19 \sqrt{7}$

Decimal Form:

50.26927491 \dots

$50.26927491 \dots$

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

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