describe how you would estimate the square root of a number that is not a perfect square without using a calculator?

You factor out primes from the root, for example:
root 100
you can get 10 from it, or we'll use 5

100/5=20
20/5=4
root 4= 2
because there are 2 "5" we can bring that out of the root, there are 2 "2" so we bring that out too.
When a number is taking out of a root, the 2 exact same numbers become one. in this case, there are ONE 5 and ONE 2 outside the root. then You multiply 5 and 2 together, and you get 10