# What is the square root of 987?

Oct 16, 2015

$987 = 3 \cdot 7 \cdot 47$ has no square factors, so $\sqrt{987}$ cannot be simplified.

$\sqrt{987}$ is an irrational number whose square is $987$

$\sqrt{987} \approx 31.417$

#### 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