An equation involving a radical expression in which the variable sits under a radical is called what?

• A. Polynomial Equation
• B. Radical Equation
• C. Exponential Equation
• D. Rational Equation

Answer: (B)

Radical equations are equations that include a radical expression with the variable inside the root. If you see something like a square root or cube root where the unknown appears under the root, you’re looking at a radical equation. To solve, you typically raise both sides to a power to remove the root, which can introduce extraneous solutions, so you must check your answers in the original equation. For example, sqrt(x+3) = 5 leads to x+3 = 25, so x = 22, and checking confirms it works. This is distinct from polynomial equations (no radicals involved), exponential equations (variable in the exponent), and rational equations (involving fractions of polynomials). So the described situation is a radical equation.