What is the square root of 35/36?

1 Answer
Nov 29, 2015

Answer:

#sqrt(35)/6 ~~ 0.9860133#

Explanation:

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+...))))#