Question

what is the two-decimal place approximation of square root of 31???? please help

Answer 1

make a guess g

refine the guess using:\[g_n=\frac{31+g^2}{2g}\]

when gn and gn+1 have the same positional values for n.xx you got it

Answer 2

lets say 6 is a good guess, since 6^2 is 36

(31+6^2)/(2*6) = 4.666

(31+4.666^2)/(2*4.666) = 5.654762

after a 2 or 3 runs we get to 5.567764363 as a constant result on the calculator

Answer 3

thank you1

Answer 4

lol, but since im using a calculator, we could have just done sqrt(31) = 5.567764363 ...