This method comes from the approximation of the square root by the binomial series: sqrt(A² + x) = A * sqrt(1 + x/A²) = A * (1 + x/A²)^1/2 ≅ A * (1 + x/2A²) = A + x/2A For example: sqrt(93) = sqrt(9² + 12) ≅ 9 + 12/18 ≅ 9.67
Hi, it does work with 24: Choose square root of 25, which is 5. Take 5 x 2 which is 10 as the denominator. Then, take 24-25 which is minus 1. Then take 5 - 1/10 which is 4.9. This is a special case, as 24-25 becomes a negative number. Hope this helps. Feel free to let me know if you have any more queries!
This method comes from the approximation of the square root by the binomial series:
sqrt(A² + x) = A * sqrt(1 + x/A²) = A * (1 + x/A²)^1/2 ≅ A * (1 + x/2A²) = A + x/2A
For example: sqrt(93) = sqrt(9² + 12) ≅ 9 + 12/18 ≅ 9.67
Thank you so much for explaining the binomial approximation as the basis for this fast shortcut method of computing the square root of a number.
Why do you chose the times 2? To get the denominations?
Yes, you are right! In this method, you multiply the square root of the perfect square by 2 to get the denominator.
Doesn't work with 24
Hi, it does work with 24: Choose square root of 25, which is 5. Take 5 x 2 which is 10 as the denominator. Then, take 24-25 which is minus 1. Then take 5 - 1/10 which is 4.9. This is a special case, as 24-25 becomes a negative number. Hope this helps. Feel free to let me know if you have any more queries!