Example 4

Note: x-values cannot be negative.

This means that x is an element of the set of Real Numbers.

Sometimes restrictions change as the nature of the variables in the radicand change. Let's analyze potential situations.

Defined... Reasoning...
x must be positive or zero because negative values of x give non-real values/do not exist.
Whether an x-value is positive or negative, the square of any number will always be positive.
Negative values for x raised to the power of 3 will be negative numbers. So, x must be positive or zero because negative values of x give non-real values/do not exist.

Further investigation will show that even numbered exponents on the x in the radicand will generate positive values for the radicand and odd numbered exponents on x in the radicand will result in potential negative values for the radicand. Restrictions are required to avoid the potential of a negative number in the radicand of a square root.

For further information about algebraic expressions involving radicals see Example 4 on p. 208 of Principles of Mathematics 11.