Question

Among 2^1/3, 3^1/4, 5^1/2 and 7^1/4, which is the largest number?
1. 21/3
2. 71/4
3. 51/2
4. 31/4
5. 31/2

Answer 1

Correct Answer - Option 3 : 51/2

Concept Used:

Take lcm of powers to get the largest number out of (a^m, bⁿ)

Calculations:

Numbers = 21/3, 31/4, 51/2 and 71/4,

Lcm of (3, 4, 2, 4) = 12

Multiplying powers of all numbers by 12, we get

Numbers = 2^12 × 1/3, 3^12 × 1/4, 5^12 ×1/2 and 7^12 ×1/4

⇒ Numbers = 2⁴, 3³, 5⁶ and 7³

⇒ Numbers = 16, 27, 15625 and 343

Largest number = 15625

⇒ Out of given numbers, largest number = 5^1/2

∴ The largest number is 51/2.