Simplify square root of 20+ square root of 18- square root of 5

$\sqrt{20} + \sqrt{18} - \sqrt{5}$

Simplify each term.

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

Factor $4$ out of $20$ .

$\sqrt{4 (5)} + \sqrt{18} - \sqrt{5}$

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

$\sqrt{2^{2} \cdot 5} + \sqrt{18} - \sqrt{5}$

$\sqrt{2^{2} \cdot 5} + \sqrt{18} - \sqrt{5}$

Pull terms out from under the radical.

$2 \sqrt{5} + \sqrt{18} - \sqrt{5}$

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$2 \sqrt{5} + \sqrt{9 (2)} - \sqrt{5}$

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

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

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

Pull terms out from under the radical.

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

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

Subtract $\sqrt{5}$ from $2 \sqrt{5}$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$6.47870866 \dots$

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