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Understanding the square root is essential for solving radical equations. The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 4 is 2 because when 2 is multiplied by itself (2 x 2), it yields 4. It's crucial to remember that square roots are defined to be non-negative for real numbers, so while both 2 and -2 squared equal 4, the square root of 4 is defined to be only the positive option, 2.

This knowledge is particularly useful when dealing with radical equations, where you'll often need to find the square root of a number in order to progress towards the solution. In the context of our exercise, you'll notice that even though we are squaring -2 to compare with 4, the accepted mathematical convention is to treat the square root of 4 as positive 2.

The ability to substitute values in equations is a fundamental skill in algebra. This involves replacing a variable with a given number to see if the equation balances or to simplify the expression. Consider the equation \(\sqrt{10-x}=-2\); if we're asked whether 6 is a solution, we substitute x with 6. The substitution is straightforward: \(\sqrt{10-6}\) transforms into \(\sqrt{4}\).

Through substitution, we take the abstract, variable-filled equation and turn it into a concrete, numerical expression that we can evaluate. Always pay attention to order of operations and ensure that each step is performed correctly to avoid errors in your calculations.

Evaluating expressions is the process of performing the operations in an expression to determine its value. This can involve arithmetic, like addition and subtraction, as well as more complex operations, such as calculating squares or square roots. In solving radical equations, evaluating the expression after substituting values is paramount.

In our original exercise, after substituting 6 for x, we need to evaluate \(\sqrt{4}\). The evaluation always follows mathematical rules, so it results in a positive 2, not -2, since we always consider the principal square root. The final step is to compare this value to the one on the other side of the equation, determining if the equation holds true with the given substitution. If the two sides do not match, as in this case, where we end up comparing 2 to -2, the proposed value is not a solution to the equation.