Simplify: $\sqrt{108} + \sqrt{125} - \sqrt{75}$

Analyze the question: We need to simplify each square root by pulling out perfect squares, then combine the like terms (surds with the same radicand).

Concept: √(a·b) = √a × √b. Only surds with the same number under the root can be added or subtracted.

Solution:

• √108 = √(36 × 3) = 6√3
• √125 = √(25 × 5) = 5√5
• √75 = √(25 × 3) = 5√3

Now substitute:

6√3 + 5√5 − 5√3

Combine the √3 terms:

(6√3 − 5√3) + 5√5 = √3 + 5√5

Tip: Always break each number into its largest perfect-square factor (4, 9, 16, 25, 36...). Then group the surds with the same root, just as you would group "like terms" in algebra. Options B, C and D can be eliminated quickly because the √5 term stays positive and no √2 ever appears.