Fast Square Root Estimation

Problem

Finding square roots mentally for non-perfect squares is difficult.

Solution

Find the two perfect squares it falls between, then estimate proportionally.

Benefit

Get accurate estimates (±0.5) of square roots mentally in seconds.

Example

√50:
49 < 50 < 64
7 < √50 < 8
50 is close to 49, so √50 ≈ 7.1
(Actual: 7.07)

√80:
64 < 80 < 81
8 < √80 < 9
80 is very close to 81, so √80 ≈ 8.9
(Actual: 8.94)