Equations that have variables in the radicand are called radical equations.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
And when solving radical equations, we will employ the power property of roots.
The power property states that once you isolate the radical on one side of the equation, you can raise each side of the equation to a power that is the same as the index of the radical so that the radical is eliminated.
So if we are trying to solve a square root equation, we will simply square both sides. Likewise, if we are trying to solve a cube root equation, we will just raise both sides to the power of 3.
Simple!
Moreover, we will also learn how to solve equations by “square rooting” both sides.
So what is the square root method?
Rather than factoring or using the quadratic formula or completing the square, it is sometimes easier to just apply the square root to both sides of the equation.
But, there is a warning. Whenever we take the square root to both sides of an equation we must put plus-or-minus.
Example of How to Solve a Radical Equation
Example of the Square Root Method
Because as you will recall, while the radical symbol stands for the principal or non-negative square root, if the index is an even positive integer then we must include the absolute value, which allows for both the positive and negative solution.
In other words, every positive number has two square roots: a positive square root and a negative square root.
Therefore, when we take the square root we must remember to take both the positive square root and the negative square root, as Khan Academy nicely points out, and always remember to check all proposed solutions in the original equation.
Together we will solve countless equations involving radicals.
Solving Radical Equations (How-To) – Video
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