Q19
Arrange the following surds in increasing order :
(A)
(B)
(C)
(D)
Choose the correct answer from the options given below :
Answer: D
Key idea: raise every surd to the LCM of the root orders so all become whole numbers. The orders are 3, 2, 4 and 6, so the LCM is 12. Raise each to the 12th power:
- A: \( (2^{1/3})^{12} = 2^4 = 16 \)
- B: \( (3^{1/2})^{12} = 3^6 = 729 \)
- C: \( (5^{1/4})^{12} = 5^3 = 125 \)
- D: \( (7^{1/6})^{12} = 7^2 = 49 \)
16 < 49 < 125 < 729, so A < D < C < B.
(Approximate values: 1.26, 1.38, 1.50, 1.73.)
Answer: A < D < C < B (option 4)