Python

1. On slide 11 of the file MIT6_0001F16_Lec1, we discussed about an algorithm to compute the exact square root of a number. With an initial guess, compute the exact square root of the following numbers:

a) 280

b) 179

c) 321

Make sure that the guesses which you give are not closer than 10%. Of the individual numbers in a), b) c). Find how many iterations you need to arrive at the exact square root. Also find out if any of the square root computations may diverge (you need infinite number of iterations or you may not arrive at the exact square root and may go off-track).

A NUMERICAL EXAMPLE square root of a number x is y such that y*y = x recipe for deducing square root of a number x (16) 1) Start with a guess, g 2) If g*g is close enough to x, stop and say g is the answer 3) Otherwise make a new guess by averaging g and x/g 4) Using the new guess, repeat process until close enough g*g |xlg (g+x/g)/2 9 4.17 4.17 17.36 3.837 4.0035 4.0035 16.0277 3.997 4.000002 3 16/3 6.0001 LECTURE 1