Use Newton’s Method for Square Roots to compute the square root of 157, starting from an initial guess of x 0 = 78.5, accurate to 4 decimal places. How many iterations are needed to reach this level...

Use Newton’s Method for Square Roots to compute the square root of 157, starting from an initial guess of x₀
= 78.5, accurate to 4 decimal places. How many iterations are needed to reach this level of precision?

Use the bisection algorithm to find an approximate solution z to the equation x^5.3
+ (3:5)^x  = N where N is your 7-digit phone number, and:

(a) z is correct to 2 significant figures.

(b) z is correct to 2 decimal places.