Square roots by looking
From the sub-sutra Vilokanam, By mere observation
, in Bharati Krishna Tirtha's 1965 book Vedic Mathematics. Deep dive into the sub-sutra
Try it with your numbers
When to use it
Square roots of perfect squares up to 9801.
The idea
The last digit narrows the answer to two choices. The front digits give the tens. One comparison with a square ending in 5 picks the winner.
Worked example: √5329
- …9 → 3 / 7It ends in 9, so the root ends in 3 or 7.
- 53 → 7_Front part 53: the biggest square below it is 7² = 49, so the tens digit is 7.
- √5329 = 7375² = 5625. 5329 is smaller, so pick the smaller choice: 73.
All 15 speed tricks, each with its calculator. The speed tricks use sutras from Bharati Krishna Tirtha's 1965 book Vedic Mathematics; the lessons, problems and pictures here are our own.