How do you factor and simplify the square root of 75?

We have to first find the largest square factor in the number that you are square rooting.

##75=25## x ##3##

##25## is a square number! ##25=5^2##

##sqrt75##=##sqrt25## x ##sqrt3##

##sqrt75##= ##5## x ##sqrt3## = ##5####sqrt3##

3 is a prime number and does not have any factors and thus the square root of 3 cannot be simplified further.