When solving radical equations we isolate the radical, and then square both sides of the equation.
We must always check our answers in the original equation, because squaring both sides of an equation sometimes generates an equation that has roots that are not roots of the original equation.
(The reason for using powers will become clear in a moment.) This is the same type of strategy you used to solve other, non-radical equations—rearrange the expression to isolate the variable you want to know, and then solve the resulting equation..
(This property allows you to square both sides of an equation and remain certain that the two sides are still equal.) The second is that if the square root of any nonnegative number x is squared, then you get x: Notice how you combined like terms and then squared both sides of the equation in this problem.
Sometimes you will need to solve an equation that contains multiple terms underneath a radical.
Follow the same steps to solve these, but pay attention to a critical point—square both sides of an equation, not individual terms. Following rules is important, but so is paying attention to the math in front of you—especially when solving radical equations.
Extraneous solutions may look like the real solution, but you can identify them because they will not create a true statement when substituted back into the original equation.
This is one of the reasons why checking your work is so important—if you do not check your answers by substituting them back into the original equation, you may be introducing extraneous solutions into the problem.
Take a look at this next problem that demonstrates a potential pitfall of squaring both sides to remove the radical..
Notice that the radical is set equal to −2, and recall that the principal square root of a number can only be positive.