# How do you find the square root of 10?

##### 1 Answer

Jun 26, 2016

#### Explanation:

It is an irrational number a little greater than

In fact, since

#sqrt(10) = [3;bar(6)] = 3+1/(6+1/(6+1/(6+1/(6+1/(6+1/(6+...))))))#

We can truncate this continued fraction expansion to get rational *approximations* to

For example:

#sqrt(10) ~~ [3;6] = 3+1/6 = 19/6 = 3.1bar(6)#

#sqrt(10) ~~ [3;6,6] = 3+1/(6+1/6) = 3+6/37 = 117/37 = 3.bar(162)#

Actually:

#sqrt(10) ~~ 3.16227766016837933199#