Evaluate square root of 125-2 square root of 20

$\sqrt{125} - 2 \sqrt{20}$

Simplify each term.

Rewrite $125$ as $5^{2} \cdot 5$ .

Factor $25$ out of $125$ .

$\sqrt{25 (5)} - 2 \sqrt{20}$

Rewrite $25$ as $5^{2}$ .

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

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

Pull terms out from under the radical.

$5 \sqrt{5} - 2 \sqrt{20}$

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

Factor $4$ out of $20$ .

$5 \sqrt{5} - 2 \sqrt{4 (5)}$

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

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 2$ .

$5 \sqrt{5} - 4 \sqrt{5}$

$5 \sqrt{5} - 4 \sqrt{5}$

Subtract $4 \sqrt{5}$ from $5 \sqrt{5}$ .

$\sqrt{5}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt{5}$

Decimal Form:

$2.23606797 \dots$

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