Question

What is the square root of 35/36?

Answer 1

`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+...))))`