Nichola Wiel's Method for Approximating Square Roots
Lets say you want to approximate the value of a square root that is not a perfct square like the number 44. In other words you want an approximate value of sqrt(44). You can use this method that was developed by Nichola Wiel for approximating its value.
STEP 1: Locate the values of he two adjacent perfect squares that 44 falls between, (which would be 36 and 49) and calculate their roots, which would be 6 and 7 respectively.
STEP 2: Calculate the difference between the two roots: 49-36 = 13. This will be the denominator of the fractional approximation.
STEP 3: Calculate the number of places 44 lies from, the smaller value 36: 44-36=8. This will be the numerator of your approximation.
PUT IT ALL TOGETHER: So the final approximation will be 6 8/13 or 6.615. The actual decimal value is 6.633 so you are accurate (and will generally be so) to a tenth! Sometimes you'll be accurate to a 100th!
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