# How do you find the square root of 17?

##### 1 Answer

Jun 26, 2016

We can calculate rational approximations like:

#sqrt(17) ~~ 268/65 ~~ 4.1231#

#### Explanation:

Since

It is an irrational number a little larger than

Since

#sqrt(17) = [4;bar(8)] = 4+1/(8+1/(8+1/(8+1/(8+1/(8+1/(8+...))))))#

You can terminate this continued fraction expansion early to get rational *approximations* to

For example:

#sqrt(17) ~~ [4;8,8] = 4+1/(8+1/8) = 4+8/65 = 268/65 = 4.1bar(230769)#

Actually:

#sqrt(17) ~~ 4.12310562561766054982#