Question

Estimate square root of 14 to the nearest integer.

Answer 1

We may calculate the given, square root of 14, by using our calculators directly. The answer to this is 3.74165. If this number is rounded to the nearest integer, the answer would be 4 because the number that appears after the decimal point is 7 and is greater than 5. 

Answer 2

Without using the calculator, you can estimate square root of 14 to the nearest integer as follows:

1. You know that

$3^2=9,\\ 4^2=16.$

2. 9<14<16.

3. Then $\sqrt{9}<\sqrt{14}<\sqrt{16}$

that is equivalent to

$3<\sqrt{14}<4.$

4. Since

$14-9=5, \\ 16-14=2,$

you can conclude that $\sqrt{14}$ is closer to 4 than to 3 and the nearest integer is 4.

Answer: $\sqrt{14} \approx 4.$