Basic Math Examples

$\sqrt{80} + \sqrt{20}$

Step 1

Simplify each term.

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Step 1.1

Rewrite

$80$ as

$4^{2} \cdot 5$ .

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Step 1.1.1

Factor

$16$ out of

$80$ .

$\sqrt{16 (5)} + \sqrt{20}$

Step 1.1.2

Rewrite

$16$ as

$4^{2}$ .

$\sqrt{4^{2} \cdot 5} + \sqrt{20}$

$\sqrt{4^{2} \cdot 5} + \sqrt{20}$

Step 1.2

Pull terms out from under the radical.

$4 \sqrt{5} + \sqrt{20}$

Step 1.3

Rewrite

$20$ as

$2^{2} \cdot 5$ .

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Step 1.3.1

Factor

$4$ out of

$20$ .

$4 \sqrt{5} + \sqrt{4 (5)}$

Step 1.3.2

Rewrite

$4$ as

$2^{2}$ .

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

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

Step 1.4

Pull terms out from under the radical.

$4 \sqrt{5} + 2 \sqrt{5}$

$4 \sqrt{5} + 2 \sqrt{5}$

Step 2

Add

$4 \sqrt{5}$ and

$2 \sqrt{5}$ .

$6 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{5}$

Decimal Form:

$13.41640786 \dots$

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