Radical equations
When you want to solve an equation with containing a radical expression you have to isolate the radical on one side from all other terms and then square both sides of the equation.
Example
3√x=9
√x=93=3
(√x)2=(3)2
x=9
When you square a radical equation you sometimes get a solution to the squared equation that is not a solution to the original equation. Such an equation is called an extraneous solution. Remember to always check your solutions in the original equation to discard the extraneous solutions.
Example
√2−x=x
(√2−x)2=x2
2−x=x2
x2+x−2=0
x=−1±√12−4⋅(−2)2
x=−1±√1+82
x1=−1+√92=−1+32=22=1
x2=−1−√92=−1−32=−42=−2
Here we've got two solutions x = 1 or x = (-2). We check both solutions in the original equation to test whether they are true solutions or extraneous solutions.
√2−1?=1or√2−(−2)?=−21=12=−2Wrong!
As we could see when we checked our numbers in the original equation x =1 is the only true solution for this equation and that x = -2 is an extraneous solution.
Video lesson
Solve the radical equation
√10−x=x+2