Question

simplify the radical expression.

1. $sqrt{50} - sqrt{18}$

Explanation:

Step1: Simplify $\sqrt{50}$

Factor 50 into $25 \times 2$, so $\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}$

Step2: Simplify $\sqrt{18}$

Factor 18 into $9 \times 2$, so $\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}$

Step3: Subtract the simplified terms

Substitute the simplified radicals into the original expression: $5\sqrt{2} - 3\sqrt{2} = (5-3)\sqrt{2}$

Answer:

$2\sqrt{2}$