Evaluate square root of 5+ square root of 45

$\sqrt{5} + \sqrt{45}$

Step 1

Simplify each term.

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

Factor $9$ out of $45$ .

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

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

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

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

Pull terms out from under the radical.

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

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

Step 2

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

$4 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{5}$

Decimal Form:

$8.94427190 \dots$

Related Questions