# How do you use linear approximation to the square root function to estimate square roots #sqrt 8.95#?

##### 1 Answer

The linear approximation of

#### Explanation:

The function we want to approximate is

We want to estimate

Although we can easily find

By now you may be anxious for me to say, "we'll use

So

For the linearization we'll need

The linearization of

Our estimate is

# = 3-0.05/6 = 3- 0.008bar(3)#

# = 2.991bar6#

Round to the desired accuracy. Keep in mind that this is an estimate for the desired number