# What is the square root of 780?

##### 1 Answer

Oct 23, 2015

#### Explanation:

#sqrt(780) = sqrt(2^2*195) = sqrt(2^2)sqrt(195) = 2sqrt(195)#

Now

#sqrt(195) = [13;bar(1;26)] = 13 + 1/(1+1/(26+1/(1+1/(26+...))))#

We can approximate

#sqrt(195) ~~ [13;1,26,1] = 13 + 1/(1+1/(26+1/1)) = 13+27/28 = 391/28 = 13.96dot(4)2815dot(7)#

So:

#sqrt(780) = 2sqrt(195) ~~ 391/14 = 27.9dot(2)8571dot(4) ~~ 27.93#