# How do you simplify #sqrt(68)#?

##### 1 Answer

May 23, 2016

#### Explanation:

If

#sqrt(ab) = sqrt(a)sqrt(b)#

The prime factorisation of

#68=2xx2xx17#

So we have:

#sqrt(68) = sqrt(2^2*17) = sqrt(2^2)*sqrt(17) = 2sqrt(17)#

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

You can terminate this expansion at any point to give a rational approximation. For example:

#sqrt(17) ~~ [4;8,8] = 4+1/(8+1/8) = 268/65 ~~ 4.1231#