Question

simplify the radical expression.

1. $sqrt{125} - sqrt{80}$

Explanation:

Step1: Simplify $\sqrt{125}$

Factor 125 into $25 \times 5$, so $\sqrt{125} = \sqrt{25 \times 5} = \sqrt{25} \times \sqrt{5} = 5\sqrt{5}$

Step2: Simplify $\sqrt{80}$

Factor 80 into $16 \times 5$, so $\sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4\sqrt{5}$

Step3: Subtract the simplified terms

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

Answer:

$\sqrt{5}$