Find the Exact Value square root of 45- square root of 20+ square root of 125

$\sqrt{45} - \sqrt{20} + \sqrt{125}$

Step 1

Simplify each term.

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

Factor $9$ out of $45$ .

$\sqrt{9 (5)} - \sqrt{20} + \sqrt{125}$

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

$\sqrt{3^{2} \cdot 5} - \sqrt{20} + \sqrt{125}$

$\sqrt{3^{2} \cdot 5} - \sqrt{20} + \sqrt{125}$

Pull terms out from under the radical.

$3 \sqrt{5} - \sqrt{20} + \sqrt{125}$

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

Factor $4$ out of $20$ .

$3 \sqrt{5} - \sqrt{4 (5)} + \sqrt{125}$

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

$3 \sqrt{5} - \sqrt{2^{2} \cdot 5} + \sqrt{125}$

$3 \sqrt{5} - \sqrt{2^{2} \cdot 5} + \sqrt{125}$

Pull terms out from under the radical.

$3 \sqrt{5} - (2 \sqrt{5}) + \sqrt{125}$

Multiply $2$ by $- 1$ .

$3 \sqrt{5} - 2 \sqrt{5} + \sqrt{125}$

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

Factor $25$ out of $125$ .

$3 \sqrt{5} - 2 \sqrt{5} + \sqrt{25 (5)}$

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

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

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

Pull terms out from under the radical.

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

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

Step 2

Simplify by adding terms.

Subtract $2 \sqrt{5}$ from $3 \sqrt{5}$ .

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

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

$6 \sqrt{5}$

$6 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{5}$

Decimal Form:

$13.41640786 \dots$

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