That is, the definition of the square root says that the square root will spit out only the positive root. While either of +2 and −2 might have been squared to get 4, "the square root of four" is defined to be only the positive option, +2. The check of the solution x = –15 is left to you.Note that the value of the simplified radical is positive. Raise both sides of the equation to the index of the radical in this case, cube both sides. Since radicals with odd indexes can have negative answers, this problem does have solutions. Isolate the radical involving the variable. This can be solved either by factoring or by applying the quadratic formula. There is no solution, since cannot have a negative value. This quadratic equation now can be solved either by factoring or by applying the quadratic formula. Raise both sides to the index of the radical in this case, square both sides. These solutions are called extraneous solutions. If there is still a radical equation, repeat steps 1 and 2 otherwise, solve the resulting equation and check the answer in the original equation.īy raising both sides of an equation to a power, some solutions may have been introduced that do not make the original equation true. Raise both sides of the equation to the index of the radical. If more than one radical expression involves the variable, then isolate one of them. Isolate the radical expression involving the variable.
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