What does the small number on top of the square root symbol mean?

This is the inverse function of $a^n$. Hence $\sqrt[n]a$ means, you look for a number $b$, which when multiplied $n$ times with itself results in $a$.

For instance: We know that $2^3 = 8$, so $\sqrt[3]8 = 2$, $\sqrt[5]{-1}=-1$ because $(-1)^5 = -1$. $\sqrt[4]3 \approx 1.31607$ because $1.31607^4 \approx 3$.

If there is no number at the top of the root symbol, it means $n=2$, so $\sqrt[2]a = \sqrt a$.

It means that instead of the "square root of a" you are now considering the "nth root of a". This is the same as writing $a^{1 \over n}$. And just like the square root is "undone" by applying a squared term, i.e., $(\sqrt a)^2 = a$, so the nth root is "undone" by applying the nth power, i.e., $(\sqrt[n] a)^n = a$.

$\sqrt[n] a$=$a^ \frac 1 n$

Also,if $\sqrt[n] a$=$x$ then $x^n=a$