What is the square root of 99 to the nearest tenth?
A. 9.9
B. 10.9
C. 11.9
D. 12.9
The correct answer and explanation is:
To find the square root of 99 to the nearest tenth, we first need to determine the square root of 99 using a calculator or estimation.
The square root of 99 is approximately 9.949874. When rounded to the nearest tenth, this gives us 9.9.
Now let’s understand why this happens. The square root of a number is the value that, when multiplied by itself, equals the original number. In the case of 99, we know that 9 multiplied by 9 is 81, and 10 multiplied by 10 is 100. So, the square root of 99 must be between 9 and 10. More specifically, it is closer to 10 than to 9, as the square of 9.9 is 98.01, which is much closer to 99 than the square of 9 is (which is 81).
To find the square root of 99 more precisely, we can use a calculator, which gives us the value of 9.949874. When rounding this to the nearest tenth, we look at the digit in the hundredths place. If it is 5 or higher, we round up. Since the hundredths place in this case is 4, we round down to 9.9.
Thus, the correct answer is A. 9.9.
This kind of estimation is helpful when you don’t have a calculator and need to quickly approximate the square root of a number. The key is understanding the proximity of the number to known perfect squares, in this case, 81 (9²) and 100 (10²).