Approximate the square root of 64.3, y=x^(1/2). Starting point is the square root of 64.

Answer 1

y = x^(1/2)
dy/dx = (1/2)x^(-1/2)

dy = 1/(2√x) dx
when x = 64, dx = .3

dy = (1/2√64)(.3) = (1/16)(.3) = appr .01875

so √64.3 = 8.01875

actual √64.3 by calculator = 8.018729

error is .000022

Answer 2

64.31