Find the nearest perfect square on either side of the given value.
20
To estimate sqrt(415) to the nearest whole number, we need to look at the nearest perfect squares. The two nearest perfect squares are 400 and 441. We can compare these values to 415 to make our estimation.
We know that sqrt(415) is somewhere between 20 and 21. Next, we have to think about to which perfect square it is closer.
400+15 → 415+26 → 441
Because 415 is closer to 400, sqrt(415) is closer to sqrt(400). Therefore, the nearest whole number is 20.
