Mentally finding square root of numbers using interpolation.
Suppose the number is 73.
Lets use interpolation. The nearest perfect square number is 64. So the answer is 8.xx, aka 8 point something.
Lets figure out the approximate value of "point something" using interpolation.
Find the midway of the difference between the two numbers.
Difference : 73-64 = 9. Midway is 4.5.
That's mid point between the two numbers. Next we need to scale it down at the square root range for the answer. Therefore divide it by our first answer 8.
4.5 / 8 = 0.56
The answer is 8.56
Real answer is 8.54. Very much near.
Had I wanted to perform the division in my head, I would have watched that 4.5 is almost half way between 8. Therefore 4.5/8 = 0.52 possibly.
Thus the answer 8.5 approximately.
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