Simplify square root of 20- square root of 80+ square root of 125

$\sqrt{20} - \sqrt{80} + \sqrt{125}$

Step 1

Simplify each term.

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

Factor $4$ out of $20$ .

$\sqrt{4 (5)} - \sqrt{80} + \sqrt{125}$

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

$\sqrt{2^{2} \cdot 5} - \sqrt{80} + \sqrt{125}$

$\sqrt{2^{2} \cdot 5} - \sqrt{80} + \sqrt{125}$

Pull terms out from under the radical.

$2 \sqrt{5} - \sqrt{80} + \sqrt{125}$

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

Factor $16$ out of $80$ .

$2 \sqrt{5} - \sqrt{16 (5)} + \sqrt{125}$

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

$2 \sqrt{5} - \sqrt{4^{2} \cdot 5} + \sqrt{125}$

$2 \sqrt{5} - \sqrt{4^{2} \cdot 5} + \sqrt{125}$

Pull terms out from under the radical.

$2 \sqrt{5} - (4 \sqrt{5}) + \sqrt{125}$

Multiply $4$ by $- 1$ .

$2 \sqrt{5} - 4 \sqrt{5} + \sqrt{125}$

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

Factor $25$ out of $125$ .

$2 \sqrt{5} - 4 \sqrt{5} + \sqrt{25 (5)}$

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

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

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

Pull terms out from under the radical.

$2 \sqrt{5} - 4 \sqrt{5} + 5 \sqrt{5}$

$2 \sqrt{5} - 4 \sqrt{5} + 5 \sqrt{5}$

Step 2

Simplify by adding terms.

Subtract $4 \sqrt{5}$ from $2 \sqrt{5}$ .

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

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

$3 \sqrt{5}$

$3 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{5}$

Decimal Form:

$6.70820393 \dots$

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