Radical equations are equations that have a variable inside a square root or another type of radical. The goal of solving a radical equation is to find the value of the variable that makes the equation true.

To solve a radical equation, we usually start by isolating the radical expression on one side of the equation. Then we can square both sides of the equation to eliminate the radical. However, it's important to keep in mind that squaring both sides of an equation can sometimes introduce extraneous solutions, which are solutions that don't actually work in the original equation.

Let's look at an example:

√(x + 4) = 6

To isolate the radical expression, we can start by subtracting 4 from both sides:

√(x + 4) - 4 = 6 - 4

Simplifying, we get:

√(x + 4) - 4 = 2

Next, we can square both sides of the equation:

[√(x + 4) - 4]^2 = 2^2

Expanding the left side of the equation, we get:

(x + 4) - 8√(x + 4) + 16 = 4

Simplifying further, we get:

x - 8√(x + 4) + 12 = 0

Now we have a polynomial equation that we can solve using the techniques we discussed earlier. Once we find the solutions, we need to check them in the original equation to make sure they work.

Radical equations can be a bit tricky, but with practice, your 12-year-old will be able to master them!