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Simplify 3 square root of 5+ square root of 20- square root of 125

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

Step 1

Simplify each term.

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.

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

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.

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

Multiply

$5$ by

$- 1$ .

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

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

Step 2

Simplify by adding terms.

Add

$3 \sqrt{5}$ and

$2 \sqrt{5}$ .

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

Subtract

$5 \sqrt{5}$ from

$5 \sqrt{5}$ .

$0$

$0$

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