Some integers, like 4 or 25, have integer square roots. More commonly, though, the square root of an integer will be an irrational number; for example, $$\sqrt{5}=2.236067977499789696409174\dots$$ When this is the case, we don't always want to express the root as a decimal, for two reasons: it becomes unwieldy, and we lose numerical precision through rounding error. Instead, and especially during a calculation, we might want to express it as an unevaluated square root (or more generally, a cube root, or fourth root, etc); such an unevaluated root is called a surd.
Surds can sometimes be simplified; for example:
\begin{eqnarray} \sqrt{45}&=&\sqrt{3^2\times5}\\ &=&\sqrt{3^2}\times\sqrt{5}\\ &=&3\sqrt{5}. \end{eqnarray}
In general, it's easier to divide a decimal by an integer than the other way round. For this reason, it makes sense to get rid of any surds in the denominators of fractions before evaluating them as decimals, a process known as rationalisation. For example: