Evaluate square root of 45+ square root of 80

$\sqrt{45} + \sqrt{80}$

Step 1

Simplify each term.

Rewrite $45$ as $3^{2} \cdot 5$ .

Factor $9$ out of $45$ .

$\sqrt{9 (5)} + \sqrt{80}$

Rewrite $9$ as $3^{2}$ .

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

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

Pull terms out from under the radical.

$3 \sqrt{5} + \sqrt{80}$

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

Factor $16$ out of $80$ .

$3 \sqrt{5} + \sqrt{16 (5)}$

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

$3 \sqrt{5} + \sqrt{4^{2} \cdot 5}$

$3 \sqrt{5} + \sqrt{4^{2} \cdot 5}$

Pull terms out from under the radical.

$3 \sqrt{5} + 4 \sqrt{5}$

$3 \sqrt{5} + 4 \sqrt{5}$

Step 2

Add $3 \sqrt{5}$ and $4 \sqrt{5}$ .

$7 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$7 \sqrt{5}$

Decimal Form:

$15.65247584 \dots$

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