Evaluate square root of 80+ square root of 20

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

Simplify each term.

Rewrite $80$ as $4^{2} \cdot 5$ .

Factor $16$ out of $80$ .

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

Rewrite $16$ as $4^{2}$ .

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

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

Pull terms out from under the radical.

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

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

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

Rewrite $4$ as $2^{2}$ .

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

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

Pull terms out from under the radical.

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

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

Add $4 \sqrt{5}$ and $2 \sqrt{5}$ .

$6 \sqrt{5}$

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{5}$

Decimal Form:

$13.41640786 \dots$

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