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How to Solve Single & Double Radical Equations

A radical equation is any equation that possesses terms placed under the radical symbol. The radical symbol indicates that the root of a quantity must be taken. The most commonly encountered radical is the square root. Algebraic manipulation allows for the radicals to be removed from an equality so that the expression is left in its simplest form. Radical equalities are first presented in intermediate algebra courses as a means for showing the relationships between roots and exponents.

Instructions

    • 1

      Simplify the equation by reducing any fractions or combining like terms.

    • 2

      Isolate the single or double radical expression on one side of the equation by moving all terms that are not part of it to the opposite side of the equation.

    • 3

      Examine the radical symbols in the equation to determine the indexes of the radicals present. The index is indicated by a superscript in the upper-left corner of the radical symbol. If no index is present, it is understood to be a value of two.

    • 4

      Raise both sides of the equation to an exponent equal to the outermost radical, if two are present. This removes the radical symbol, leaving behind only the underlying value and the second radical, if it is a double radical equation. If the equation was a single radical equation the expression may now be solved algebraically for a variable.

    • 5

      Examine the index of the inner radical, if one is present, and raise both sides of the equation to an exponent equal to that index. This is necessary only in the case of the double radical. Upon completion of the second exponentiation the equation may be algebraically simplified to solve for an unknown variable.

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