Most of us were taught to just memorize square roots, but the "distance" between square numbers follows a perfect, predictable pattern of odd numbers:
0 to 1 (+1)
1 to 4 (+3)
4 to 9 (+5)
9 to 16 (+7)
16 to 25 (+9)
25 to 36 (+11)
36 to 49 (+13)
49 to 64 (+15)
64 to 81 (+17)
The "Cheat Code" for non-perfect squares:
If you need the square root of something like 27, you can use this pattern to get an answer accurate to 99% in seconds.
(The actual answer is 5.196. You're off by only 0.004).
It works for anything. √50? Closest is 49 (7²). Reminder is 1. Double the root is 14. Answer is 7 ¹/₁₄ (\~7.07).
Once you see the pattern, you can't unsee it. I’ve been using this trainer to get my speed up and it’s weirdly addictive once you stop fearing the numbers:
chucny.github.io/square-root-trainer (this trainer was programmed by me)
Note: I'll take no credits for inventing this method. This is common sense, and a similar method was invented by Isaac Newton and the Babylonians 2000 years a go.
What is √78.932? Now you can answer it in a second!