Question

What is the square root of 987?

Answer 1

`987 = 3 * 7 * 47` has no square factors, so `sqrt(987)` cannot be simplified.

`sqrt(987)` is an irrational number whose square is `987`

`sqrt(987) ~~ 31.417`

Explanation:

In common with all irrational square roots, `sqrt(987)` cannot be expressed as a repeating decimal, but it can be expressed as a repeating continued fraction...

`sqrt(987) = [31;bar(2,2,2,62)] = 31+1/(2+1/(2+1/(2+1/(62+1/...))))`

We can use this continued fraction to give us an approximation by truncating it just before it repeats...

`sqrt(987) ~~ [31;2,2,2] = 31+1/(2+1/(2+1/2)) = 31+1/(2+2/5) = 31+5/12 = 377/12 = 31.41dot(6) ~~ 31.417`