The square root of positive numbers eli5

Question

Explain to me like I’m 5, how to determine the square root of a random positive number. And I don’t mean common sense like 16=4, I need to understand the logic.

In: 6

Answer 1

Well you might want the proper definition of powers. a^b = c^[b×log_c(a)]. Since c could be anything we can use the exp function. a^b = e^[b×ln(a)]. A square root would be b=0.5. Of course computing the values of the exp function and the ln function is also difficult to do by hand, but this is the general form of powers. a and b could be any real number and this formula will work.