# How do you use linear approximation to the square root function to estimate square roots #sqrt 4.400#?

##### 2 Answers

#### Answer:

66.33, nearly.

#### Explanation:

Using binomial expansion,

Here, choose a = 66 and b = 44.

Now,

Note that the error is of order 66(1/198)^2=O(.002), nearly.

#### Answer:

The linear approximation is a form of (or a way of thinking about) the equation of a tangent line.

#### Explanation:

For function,

Note that the equation of the line tangent to the graph at

We are not told what to use for

We want

In this case, we want a number close to

The 'obvious' (once you see it) choice is

So,

And we finish with

**If there is a typo in the question**

If the question should ask us to approximate

A bit more arithmetic will show that

Since

OR

To get a rough estimate use