Radical Functions: Solving Radical Equations and Inequalities

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How do we know if a given value is the solution to a radical equation? If the first thing you think of is to test the value, you are absolutely correct. For example, given the equation twelve equals four square root of the quantity two x plus one and a possible solution of x = 4, check to see if the solution is correct.

We will substitute x = 4 into our equation.

Twelve equals four square root of the quantity two x plus one. Twelve equals four square root of the quantity two times four plus one. Twelve equals four square root of the quantity eight plus one. Twelve equals four square root of nine. Twelve equals four times three. Twelve equals twelve.

By working through the substitution process we find that x = 4 is a solution to the equation twelve equals four square root of the quantity two x plus one.