JEE Main Maths: Indices and Surds / Basic Algebra questions with solutions

Q1. Evaluate (5*(8^(1/3) + 27^(1/3))³)^(1/4).

1. 3
2. 6
3. 5
4. 4

Answer: 5

8^(1/3) = 2 and 27^(1/3) = 3, so the sum is 5. Then (8^(1/3) + 27^(1/3))³ = 5³ = 125. The expression becomes (5 * 125)^(1/4) = (625)^(1/4) = (5⁴)^(1/4) = 5.