# How do you approximate #sqrt3#?

##### 1 Answer

Use a variant of Newton Raphson to construct a sequence of rational approximations and stop when you have enough significant digits.

#### Explanation:

In the case of finding an approximation for

If you apply this using decimals then you quickly run into choices as to where to truncate your decimals, etc.

If you apply it using fractions, then you frequently find yourself multiplying up the numerator and denominator to simplify the fractions.

Alternatively, notice that if

So use:

It can happen (in early iterations) that

For

Then:

Then