# How do you approximate #-sqrt30#?

##### 2 Answers

#### Answer:

Let's forget the

#### Explanation:

Now

So the answer must be between

Since

My first approximation would be

The calculator answer is

Not bad!

#### Answer:

Use Newton Raphson method to find a sequence of approximations for

#### Explanation:

The Newton-Raphson method, specialised to finding square roots boils down to choosing a reasonable first approximation

where

In our case let us choose

Then:

Notice that the number of significant digits roughly doubles on every iteration.

Actually, if we want to use rational approximations,

it is nicer to write

optionally dividing

That avoids some of the messy fractions.