Basic Math Examples

3 \sqrt{180} + \sqrt{80}

$3 \sqrt{180} + \sqrt{80}$

Step 1

Simplify each term.

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Step 1.1

Rewrite

180

$180$ as

6^{2} \cdot 5

$6^{2} \cdot 5$ .

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Step 1.1.1

Factor

36

$36$ out of

180

$180$ .

3 \sqrt{36 (5)} + \sqrt{80}

$3 \sqrt{36 (5)} + \sqrt{80}$

Step 1.1.2

Rewrite

36

$36$ as

6^{2}

$6^{2}$ .

3 \sqrt{6^{2} \cdot 5} + \sqrt{80}

$3 \sqrt{6^{2} \cdot 5} + \sqrt{80}$

3 \sqrt{6^{2} \cdot 5} + \sqrt{80}

$3 \sqrt{6^{2} \cdot 5} + \sqrt{80}$

Step 1.2

Pull terms out from under the radical.

3 (6 \sqrt{5}) + \sqrt{80}

$3 (6 \sqrt{5}) + \sqrt{80}$

Step 1.3

Multiply

6

$6$ by

3

$3$ .

18 \sqrt{5} + \sqrt{80}

$18 \sqrt{5} + \sqrt{80}$

Step 1.4

Rewrite

80

$80$ as

4^{2} \cdot 5

$4^{2} \cdot 5$ .

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Step 1.4.1

Factor

16

$16$ out of

80

$80$ .

18 \sqrt{5} + \sqrt{16 (5)}

$18 \sqrt{5} + \sqrt{16 (5)}$

Step 1.4.2

Rewrite

16

$16$ as

4^{2}

$4^{2}$ .

18 \sqrt{5} + \sqrt{4^{2} \cdot 5}

$18 \sqrt{5} + \sqrt{4^{2} \cdot 5}$

18 \sqrt{5} + \sqrt{4^{2} \cdot 5}

$18 \sqrt{5} + \sqrt{4^{2} \cdot 5}$

Step 1.5

Pull terms out from under the radical.

18 \sqrt{5} + 4 \sqrt{5}

$18 \sqrt{5} + 4 \sqrt{5}$

18 \sqrt{5} + 4 \sqrt{5}

$18 \sqrt{5} + 4 \sqrt{5}$

Step 2

Add

18 \sqrt{5}

$18 \sqrt{5}$ and

4 \sqrt{5}

$4 \sqrt{5}$ .

22 \sqrt{5}

$22 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

22 \sqrt{5}

$22 \sqrt{5}$

Decimal Form:

49.19349550 \dots

$49.19349550 \dots$

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

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