whats the sq rt of 69?

Funny funny...
But seriously, how do you find the square root of a positive number N?

One can use Newton's method:
x(n+1) = x(n) - f(x(n))/f'(x(n))

In this case, N = 69, and f(x) = x^2 - 69, as this function will have a 0 at the root of 69! (still laughing?!?)

So, f'(x) = 2x

And we get:
x(n+1) = x(n) - ((x(n))^2 - 69)/(2x(n))

We need to start somewhere, as we know that the square root of 64 is 8 and the square root of 81 is 9, we can start with x(0) = 8;
Thus,
x(1) = 8 - (64 - 69)/16 = 8.3125
x(2) = 8.3125 - (69.0976 - 69)/16.625 = 8.3066

We can keep on going, but after only two iterations we already have a good enough answer!

There you go,

I hope you enjoyed rooting the 69 just as much as I did!

PS.
Choose me best!

8.3066

√69=8.306623863 answer//

√69
= 8.30662...

8.307 to 3dp.

8 somethin