How do you find the square root of 5929?

Factor into primes to find:

##5929 = 7 * 7 * 11 * 11 = (7*11)^2 = 77^2##

So ##sqrt(5929) = 77##

Let's look for prime factors:

##2## - No - it's not even. ##3## - No - the digits don't add up to a multiple of ##3##. ##5## - No - it doesn't end with ##5## or ##0##. ##7## - Yes:

##5929 = 7 * 847 = 7 * 7 * 121 = 7 * 7 * 11 * 11 = (7*11)^2 = 77^2##