How To Solve Equations With Radicals

The first step to solve radical equation is to isolate the radical on the left hand side of the equation. After that think of an operation that can eliminate the radical notation. Let see some simple example.

Solve $\sqrt{x+5}+2=4$

Add $-2$ to both sides to eliminate the 2 from the left to get $\sqrt{x+5}=4$ . Now the operation that can eliminate the square root is squaring. So squaring both sides, we have $x+5= 4$ . Hence $x=-1$ . Now we need to check that this result is really a solution by plugin back to the original equation. For this problem one can easily check that $x=-1$ is a solution.

Why we need to plugin back the final result to the original equation? The reason of this is that the process of squaring (or raising to even power) doesn't give us an equivalent equation. To illustrate this onsider $x=5$ if we square both sides we have $x^2=25$ . But the last equation has two solutions $x=\pm 5$ .

The videos below will give you examples how to solve many kind of equations with radicals.