Estimate the square root of 83 to the nearest whole
The correct answer and explanation is:
The square root of 83 is approximately 9 when rounded to the nearest whole number.
Explanation:
To estimate the square root of a number, especially when it is not a perfect square, we start by identifying two perfect squares near the number. In this case, the perfect squares closest to 83 are:
- 81 (which is 929^2) and
- 100 (which is 10210^2).
The square root of 81 is exactly 9, and the square root of 100 is exactly 10. Since 83 is closer to 81 than to 100, we can reasonably estimate that the square root of 83 is a bit more than 9 but less than 10. However, when rounding to the nearest whole number, we would round 9.1, 9.2, etc., down to 9.
To get a more accurate estimate, you can use methods such as the Newton-Raphson method or interpolation, but for rounding to the nearest whole number, simply considering the nearest perfect squares gives a quick and easy estimate.
By further calculating:
- The square of 9.1 is 82.81
- The square of 9.2 is 84.64
Since 83 is closer to 82.81, we can confirm that the square root of 83 is approximately 9 to the nearest whole number.
In conclusion, the square root of 83, when rounded to the nearest whole number, is 9.