This morning, I tried to abstract myself from my computer while trying to calculate sqrt(1.81).
I came up with what I thought to be a genius method. I tried to find B such as (1+B)^2=1.81. Then I ended up calculating the discriminant of 1+2B+B^2 and had 4*1.81. Sounded funny at first, but upon calculating the positive solution amongst the 2 possible ones, I ended up with (-2+2sqrt(1.81))/2 = ... sqrt(1.81)-1. Upon replacing in the initial equation, one gets (1+sqrt(1.81)-1)^2 = (sqrt(1.81))^2 = 1.81.

I'm sorry for having let you down, dear pasokon. Please forgive me.

  • 1
    Why so complicated?

    Temporarily shift the decimal point two places in your question and shift it back by one place in the answer.

    I assume you know the square root of 2 is around 1.414?

    So estimate the square root by starting a little lower.

    14 squared is 196.
    13 squared is 169.

    You need a number between those two, call it 13.5.

    Shift the decimal place back by one and a close guess is 1.35 (which when squared is 1.82).

    Isn't that a close enough approximation?
  • 0
    When taking into account that in what I want to do, there are lots of square roots to calculate, I really prefer to minimize the errors in the calculation to get a really close result.
    And when I mean lots of square roots, it means added one to another, multiplicated together,...
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