Answer:
B. 11
Explanation:
You want the integer near √124.
Squares
Nearby squares are ...
- 10² = 100
- 11² = 121
- 12² = 144
This means the square root of 124 will lie between 11 and 12. Since 124 is closer to 121 than it is to 144, the square root of 124 will be closer to 11 than to 12.
The closest integer approximation to √124 is 11.
__
Additional comment
For an integer n = a² +b, an approximate square root will lie between ...
If you have an approximation of the root r, a better approximation will be ...
a +b/(a+r)
This means the square root of 124 = 11²+3 will be between 11 3/23 and 11 3/22. In decimal, these values are 11.1304 and 11.1364. Using the first of these for one iteration of the root, we get √124 ≈ 11 69/509 ≈ 11.13556. The actual root is near 1.13553.