The square root of 248 should lie between :
(A) 13 and 14
(B) 14 and 15
(C) 15 and 16
(D) 16 and 17
The correct answer and explanation is:
To find where the square root of 248 lies, let’s estimate it.
We know that:
- The square root of 225 is 15, since 152=22515^2 = 225.
- The square root of 256 is 16, since 162=25616^2 = 256.
248 is between 225 and 256, so the square root of 248 must be between 15 and 16.
More specifically, since 248 is closer to 225 than to 256, the square root of 248 will be closer to 15.
To refine the estimate, let’s try squaring numbers between 15 and 16:
- 15.72=246.4915.7^2 = 246.49
- 15.82=249.6415.8^2 = 249.64
So, the square root of 248 is approximately 15.8, which confirms that it lies between 15 and 16.
Therefore, the correct answer is (C) 15 and 16.