Simplify $\sqrt{27}$ + $\frac{3}{\sqrt{3}}$

Analyze the question: We need to simplify √27 + 3/√3 and match it to an option.

Concept: Simplify each term to a multiple of √3 by:

• Pulling out perfect squares from under the root.
• Rationalising the denominator (multiply top and bottom by the root).

Solution:

Step 1: Simplify √27 √27 = √(9 × 3) = 3√3

Step 2: Simplify 3/√3 3/√3 = (3 × √3)/(√3 × √3) = 3√3/3 = √3

Step 3: Add the results 3√3 + √3 = 4√3

Answer: The result is 4√3, which is option A.

Tip: When you see surds like √27, √12, or √48, always break them into (perfect square × another number) first. Once all the surds share the same root, such as √3, you can add or subtract them just like "like terms" in algebra (3x + x = 4x).