Question

Which is the correct order of the following numbers, from least to greatest?

2⁢√7 √29
5 6

Answer 1

5 < 2√7 < √29 < 6

Reason: square positive numbers to compare:
- 5^2 = 25 < (2√7)^2 = 28, so 5 < 2√7.
- (2√7)^2 = 28 < (√29)^2 = 29, so 2√7 < √29.
- (√29)^2 = 29 < 6^2 = 36, so √29 < 6.