Question

Why do square roots have to be represented as fractional exponents?

Answer 1

Fractional exponents make square roots easier to simplify. For example, the square root of 1681 isn't obvious. But if you used fractional exponents and prime factorization, you would get 41.

$\sqrt{1681} = 1681^{1/2} = (41^2)^{1/2}= 41^1 = 41$