Final answer:
The square root of a number between 1.4 and 1.5 can be found by squaring the options and identifying which result falls within the range of 1.4 squared and 1.5 squared. Option a, with a square result of 2.0164, falls within the range and is closest to 1.4 squared, making it the proper choice.
Step-by-step explanation:
The question is asking for the square root of a number between 1.4 and 1.5. To identify which of the options is correct, one approach is to square each option to see if the result falls between 1.96 (1.4 squared) and 2.25 (1.5 squared). Squaring each option:
- Option a: 1.422 = 2.0164
- Option b: 1.482 = 2.1904
- Option c: 1.452 = 2.1025
- Option d: 1.522 = 2.3104
Based on these calculations, only Options a and c fall within the range, but 1.42 is closer to 1.96 than 1.45, making it the more accurate estimation. Therefore, Option a is the square root of a number between 1.4 and 1.5.