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Understanding how to solve radical equations is a critical skill in algebra. A radical equation is an equation in which a variable is under a radical sign, such as a square root.\(
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To solve a radical equation, the goal is to isolate the radical on one side and then remove it by using inverse operations. In the case of square roots, squaring both sides of the equation allows us to remove the square root and make the equation solvable.\(
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For instance, let's look at the equation \(\sqrt{x}=6\). The square root is already isolated, so there's no need for preliminary simplification steps. The next step is to square both sides of the equation, which gives us \(x=36\). Here we have eliminated the square root and solved for \(x\).\(
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It's essential to understand that when dealing with radical equations, there’s a possibility of obtaining extraneous solutions—solutions that don’t actually satisfy the original equation. That's why conducting a validation check of your answers is a crucial step.

After finding a solution to an algebraic equation, it’s vital to ensure it is a valid one. Checking the solution involves substituting it back into the original equation to confirm that it satisfies the equation.\(
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Using the previous exercise \(\sqrt{x}=6\), where we found \(x=36\), we check the solution by substituting 36 back into the original equation. We calculate \(\sqrt{36}\) and confirm that it equals 6, which matches the right side of our equation. This step verifies that our solution is correct.\(
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If, after plugging the solution back in, the left side does not equal the right side, then you likely have an extraneous solution. It’s a result of squaring both sides, a step that can introduce solutions that weren’t there in the original equation. Thus, always remember: a solution is not truly a solution until it has been verified!

When you square both sides of an equation, you're applying the power of two to each side. This is an effective method for solving equations with a square root, because squaring a square root cancels the radical, leaving the base of the radical alone.\(
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In the context of the example \(\sqrt{x}=6\), when we square both sides, we end up with \(x=36\). Nonetheless, keep in mind that when you square both sides, you're applying a non-reversible operation, which can introduce solutions that weren’t in the original set of possible answers.\(
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This is why it's possible to get extraneous solutions when working with radical equations, and it underscores the importance of verifying any solutions obtained by this process. While squaring both sides is a powerful technique, treat the solutions obtained with caution and confirm their validity to ensure they truly solve the original equation.