Simplify $\sqrt{75}$ - $\sqrt{12}$ + $\sqrt{27}$

Analyze the question: We need to simplify surds by writing each square root as a multiple of a common surd, then combine like terms.

Concept: Use √(ab) = √a × √b. Pull out perfect squares (4, 9, 16, 25, ...) from under each root.

Solution:

• √75 = √(25 × 3) = 5√3
• √12 = √(4 × 3) = 2√3
• √27 = √(9 × 3) = 3√3

Now combine:

√75 − √12 + √27 = 5√3 − 2√3 + 3√3

= (5 − 2 + 3)√3

= 6√3

Answer: The result is 6√3, which is option D.

Tip: With surd questions, break every number into (perfect square × something). If the "something" is the same for all terms (here 3), you can add and subtract the coefficients just like ordinary like terms. Memorize the squares up to 15² to spot these quickly.