One way to determine if a square root is rational or irrational is to find out if it is the square root of a perfect square.
If the number inside the square root sign is a perfect square (i.e., the square of a whole number), then the square root is rational, because we can express it as a fraction of two integers. For example, the square root of 16 is 4, which is a rational number because it can be expressed as 4/1.
If the number inside the square root sign is not a perfect square, then the square root is irrational, because it cannot be expressed as a fraction of two integers. For example, the square root of 2 is an irrational number, because it cannot be expressed as a fraction of two integers.
While rewriting the square root as a rational exponent can also be a useful technique, it is not necessary to determine if a square root is rational or irrational.