Evaluate square root of 45+ square root of 20- square root of 5

$\sqrt{45} + \sqrt{20} - \sqrt{5}$

Step 1

Simplify each term.

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

Factor $9$ out of $45$ .

$\sqrt{9 (5)} + \sqrt{20} - \sqrt{5}$

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

$\sqrt{3^{2} \cdot 5} + \sqrt{20} - \sqrt{5}$

$\sqrt{3^{2} \cdot 5} + \sqrt{20} - \sqrt{5}$

Pull terms out from under the radical.

$3 \sqrt{5} + \sqrt{20} - \sqrt{5}$

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

Factor $4$ out of $20$ .

$3 \sqrt{5} + \sqrt{4 (5)} - \sqrt{5}$

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

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

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

Pull terms out from under the radical.

$3 \sqrt{5} + 2 \sqrt{5} - \sqrt{5}$

$3 \sqrt{5} + 2 \sqrt{5} - \sqrt{5}$

Step 2

Simplify by adding terms.

Add $3 \sqrt{5}$ and $2 \sqrt{5}$ .

$5 \sqrt{5} - \sqrt{5}$

Subtract $\sqrt{5}$ from $5 \sqrt{5}$ .

$4 \sqrt{5}$

$4 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{5}$

Decimal Form:

$8.94427190 \dots$

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