SQUARE ROOTS IN YOUR HEAD
Calculating square roots in your head may appear to be a daunting task; the square root, however, appears constantly in hydraulics calculations. Fortunately, however, you can approximate square roots very simply by using the Stirling formula, which is accurate within 6 percent for numbers between 0.5 and 2. The closer the number is to 1, the more accurate the approximation. This approximation always overestimates the square root, which in the hydraulics calculations used in my articles will result in overestimating rather than underestimating values for reach, tip pressure, and so on.
The square root of a number is approximately equal to 1 plus half the difference between the number and 1. The square root of 1.6, for example, is approximately equal to 1 + (1.6 — 1 )/2 = 1 + 0.3 = 1.3; the actual value is 1.26. The square root of 0.6 is approximately equal to 1 + (0.6l)/2 = 1-0.2 = 0.8; the actual value is 0.77.
An apparently more complicated example is the calculation of (85/50). First perform the division 85/50. Simply double the numerator (85) and the denominator (50), so it becomes (2 x 85) / (2 x 50) = 170/100 = 1.7. The approximate square root of 1.7 = 1 + (0.7/2) = 1 + 0.35 = 1.35. Practice by calculating some square roots and checking your answers against the following table:
Proficiency with mental arithmetic tricks is an easy way to look like a genius!