Final answer:
Saying the square root of 14 is approximately 3 is not very reasonable because it is closer to the square root of 16, which is 4. More accurate estimates are important when precision matters, but rough approximations can be useful for quick, practical decision-making.
Step-by-step explanation:
It is not very reasonable to say that the square root of 14 is approximately 3. If we consider that the square of 3 is 9 and the square of 4 is 16, then the square root of 14 must be somewhere between 3 and 4. A more accurate estimate would be slightly less than the square root of 16, which is exactly 4. This is because 14 is closer to 16 than it is to 9. Therefore, a reasonable approximation for the square root of 14 would be a little below 4, not 3.
To understand why an approximation like √10 ≈ 3 can be useful, consider real-life scenarios where such an estimate is sufficient for making plans or decisions. For instance, if you are considering a salary of $100,000 for a third of a year, estimating 1/3 of 10 as 3 yields a rough estimation of $30,000, which is good enough for general planning.
Ultimately, while rough guesstimates are helpful in many practical situations, they are not substitutes for more exact calculations when precision is important. In the case of estimating the square root of 14, using 3 as an approximation would not be the best choice and can lead to significant errors