Final answer:
The domain of a variable under an even indexed radical requires the expression inside the radical to be non-negative. To find the domain, one must solve an inequality where the radicand is set to be greater than or equal to zero. Always verify that the resulting domain is reasonable and contains no extraneous solutions.
Step-by-step explanation:
When finding the domain of a variable under an even indexed radical, the expression inside the radical must be non-negative.The domain of a function involving an even indexed radical, such as the square root, requires that we consider the values of the variable that make the radicand (the expression under the radical) non-negative. This is because the even roots of negative numbers are not real numbers.
In mathematical terms, for an equation such as √x, where x is under a square root, the domain would be x ≥ 0, because √x is only defined for x being zero or positive. When simplifying algebraic expressions such as x² = √x, it is important to remember that this represents a case where x must be non-negative; x² simply creates a new expression equivalent to the original radical.