Square Root of 5

The square root of 5 is about 2.2361. Square roots reverse squaring and are essential in geometry and the quadratic formula.

√5 is irrational — 5 sits between the squares 4 and 9, and no whole number between their roots can multiply by itself to give 5, so the decimal never ends nor repeats. The nearer fence sits 1 away, against 4 on the other side. Rounded to two places, 2.24 misses the true value by less than one hundredth. Slanted right-triangle sides and the quadratic formula both land on roots of exactly this kind. No fraction of integers nails it either: if a ratio a/b squared gave 5, then 5 would itself be a perfect square — which the ladder above shows it is not. That property has a name, irrationality, and it is a fact about the number, not a limit of this table.