# Find the approximate value of √8.95 - Mathematics and Statistics

Find the approximate value of  sqrt8.95

#### Solution

Let f(x)=sqrtx

f(a+h)=sqrt(a+h)

we choose a=9 and h=-0.05

Then sqrt8.95=f(a+h)

But , f(a+h)~~f(a)+hf'(a)

sqrt8.95~~f(a)+hf'(a)...........(1)

Now  f(a)=sqrta=sqrt9 and h=-0.05

we have f(X)=sqrtx

f'(x)=1/(2sqrtx)

f'(a)=f'(9)=1/(2sqrt9)=1/(2xx3)=1/6

from(1)  sqrt(8.95)~~3+(-0.05)(1/6)

=3-0.0083=2.9917

=> sqrt8.95 ~~2.9917

Concept: Approximations
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