answer: solving radical equations with checking.
step-by-step explanation: basic strategy for solving radical equations is to isolate the radical term first, and then raise both sides of the equation to a power to remove the radical. (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.
there are two key ideas that you will be using to solve radical equations. the first is that if , then . (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: . (this property allows you to “remove” the radicals from your equations.)
let’s start with a radical equation that you can solve in a few steps:
, , ,