To estimate the 102−−−√
, I would look at the perfect squares __ and __ and then choose __ as a good estimate.
Responses
101 and 103; 102
100 and 121; 10.1
81 and 100; 10.2
121 and 144; 11.5
B
To estimate the value of the square root of 102, we can first identify the perfect squares that are closest to 102. Perfect squares are numbers that can be expressed as the product of an integer multiplied by itself. In this case, we can look at the perfect squares 100 and 121.
Now, let's compare the square roots of these perfect squares to 102. The square root of 100 is 10, and the square root of 121 is 11.
Since 102 falls between the two perfect squares, we can estimate that the square root of 102 is somewhere between 10 and 11. To get a more precise estimate, we can consider the distance between 102 and the two perfect squares. The difference between 102 and 100 is 2, and the difference between 102 and 121 is 19.
Based on this information, we can infer that 102 is closer to 100 than to 121. Therefore, a sensible estimate for the square root of 102 is closer to the square root of 100, which is 10.
Out of the given options, the correct answer would be: 101 and 103; 102.
To estimate the square root of 102, we need to find the perfect squares that are closest to 102. Let's consider the options provided:
1. 101 and 103: 102 is between these two numbers. This could be a good estimate, as it is the midpoint between the two perfect squares.
2. 100 and 121: 102 is closer to 100 than 121. However, taking the midpoint of these two squares gives us a larger estimate than the previous option.
3. 81 and 100: 102 is greater than both 81 and 100. This estimate is smaller than the actual square root of 102.
4. 121 and 144: 102 is less than both of these squares. This estimate is larger than the actual square root of 102.
Therefore, the best estimate considering the provided options is 101 and 103, with 102 as a good estimate for the square root of 102.