Which of the following is a radical equation?
An equation in which the variable appears in one or more radicands is a radical equation. To eliminate a radical sign, we can raise the entire expression to an even exponent. For example, to eliminate a square root, we can square both sides of the equation; to eliminate a cube root, we can cube both sides of the equation; and so on. This process is called factoring.
Another way to eliminate radicals is by multiplying both the numerator and denominator of a radical expression by its conjugate, which is an expression that contains the same variables on both sides. This will help to simplify the radical by reducing its terms. It is important to be aware of the presence of extraneous solutions when solving radical equations, and to check that the solution obtained by squaring the original expression meets the requirements of the original problem.
To avoid the possibility of extraneous solutions, we can use the property that a number multiplied by a negative number is always positive. This can be helpful when solving an equation containing radicals because it allows us to remove the negative from the answer and make it easier to solve. The final step in the process of eliminating a radical is to evaluate the coefficients on both sides of the equation to be sure that it is equal to one. If this is not the case, then it is necessary to return to the previous steps in the process to eliminate radicals from both sides of the equation.