What is the square root of 35/36?

##sqrt(35)/6 ~~ 0.9860133##

If ##a, b > 0## then ##sqrt(a/b) = sqrt(a)/sqrt(b)##

So in our case:

##sqrt(35/36) = sqrt(35)/sqrt(36) = sqrt(35)/6##

##sqrt(35) = sqrt(5*7)## cannot be further simplified since it has no square factors.

It is an irrational number, so cannot be expressed as a repeating decimal or ratio of whole numbers.

Since ##35## is of the form ##n^2-1##, its square root does take a simple form as a continued fraction:

##sqrt(35) = [5;bar(1, 10)] = 5+1/(1+1/(10+1/(1+1/(10+…))))##