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Simplify square root of 125- square root of 45+2 square root of 5

$\sqrt{125} - \sqrt{45} + 2 \sqrt{5}$

Step 1

Simplify each term.

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

Factor $25$ out of $125$ .

$\sqrt{25 (5)} - \sqrt{45} + 2 \sqrt{5}$

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

$\sqrt{5^{2} \cdot 5} - \sqrt{45} + 2 \sqrt{5}$

$\sqrt{5^{2} \cdot 5} - \sqrt{45} + 2 \sqrt{5}$

Pull terms out from under the radical.

$5 \sqrt{5} - \sqrt{45} + 2 \sqrt{5}$

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

Factor $9$ out of $45$ .

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

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

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

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

Pull terms out from under the radical.

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

Multiply $3$ by $- 1$ .

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

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

Step 2

Simplify by adding terms.

Subtract $3 \sqrt{5}$ from $5 \sqrt{5}$ .

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

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

$4 \sqrt{5}$

$4 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{5}$

Decimal Form:

$8.94427190 \dots$

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