Question

Use a linear approximation (or differentials) to estimate the given number.

radical (99.4)

Answer 1

√99.4 = √(100-.6)

The slope of y=√x is 1/2√x
at x=10, slope is .05

so, a linear approximation is

∆y/.6 = .05
∆y = .03
y-∆y = 10-.03 = 9.97

check: √99.4 = 9.96995