Restrictions on the Variable in a Radical Equation

D. Restrictions on the Variable in a Radical Equation

Recall the restrictions for variables in the radicand in the first three rows of the table below.

In the table, there are two other types of variable restrictions involving radicals that will also be useful.

	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.
		Fractions cannot have a denominator of zero (division by zero is undefined). Since the x-value is also the radicand, it cannot be negative. So, x is any Real Number greater than zero.
		The radicand x − 7 cannot have a value less than zero. So, the values for x that make the radicand greater than or equal to zero are 7 or greater.