What is the square root of 83 to the nearest tenth?
The correct answer and explanation is:
The square root of 83, to the nearest tenth, is approximately 9.1.
To calculate this, first, recall that the square root of a number is the value that, when multiplied by itself, gives the original number. In this case, the square root of 83 is a number between 9 and 10 because:
- 9² = 81
- 10² = 100
Since 83 lies between 81 and 100, the square root of 83 must lie between 9 and 10. To find a more precise value, you can use a calculator or apply numerical methods such as the method of successive approximations (also known as the Newton-Raphson method). However, for basic purposes, using a calculator gives the square root of 83 as approximately 9.110433.
To round to the nearest tenth, observe that the first decimal place is 1, which is less than 5. Therefore, the square root of 83 rounded to the nearest tenth is 9.1.
Another way to understand the rounding process is by looking at the decimal places. If the digit in the hundredths place (the second digit after the decimal point) is 5 or greater, the digit in the tenths place (the first digit after the decimal point) is increased by 1. Since the second decimal place here is a 1, we leave the 1 in the tenths place unchanged, resulting in 9.1.
So, the square root of 83, to the nearest tenth, is 9.1.