What is the square root of 987?

1 Answer
Oct 16, 2015

Answer:

#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#