Radical equations are equations involving radicals of any order. We will show examples of square roots; higher order radicals simply require more of the same work. To solve radical equations you first have to get rid of the radicals, in the case of square roots square both sides of the equation (in some cases this should be done multiple times), then refine the new equation (either linear or quadratic) and solve. One more thing to note, by squaring the equation we changed the original equation, so it is very important to check the solutions at the end.

Let’s see how it works, simply follow the steps:

1.

Simplify: eliminate the square root

2.

Refine: refine the quadratic equation after squaring the root

3.

Solve: solve the equation

4.

Verify: plug the solutions into the original equation and verify

Click here for an example:
Now let’s zoom in on how to simplify the radical. You will notice that the first step is to isolate the square root before squaring both sides of the equation:

Here’s a more advanced example that requires multiple steps to resolve the radical (

click here):

Cheers,

Michal