Evaluate square root of 80+ square root of 320

$\sqrt{80} + \sqrt{320}$

Step 1

Simplify each term.

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

Factor $16$ out of $80$ .

$\sqrt{16 (5)} + \sqrt{320}$

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

$\sqrt{4^{2} \cdot 5} + \sqrt{320}$

$\sqrt{4^{2} \cdot 5} + \sqrt{320}$

Pull terms out from under the radical.

$4 \sqrt{5} + \sqrt{320}$

Rewrite $320$ as $8^{2} \cdot 5$ .

Factor $64$ out of $320$ .

$4 \sqrt{5} + \sqrt{64 (5)}$

Rewrite $64$ as $8^{2}$ .

$4 \sqrt{5} + \sqrt{8^{2} \cdot 5}$

$4 \sqrt{5} + \sqrt{8^{2} \cdot 5}$

Pull terms out from under the radical.

$4 \sqrt{5} + 8 \sqrt{5}$

$4 \sqrt{5} + 8 \sqrt{5}$

Step 2

Add $4 \sqrt{5}$ and $8 \sqrt{5}$ .

$12 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$12 \sqrt{5}$

Decimal Form:

$26.83281572 \dots$

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