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A square root of a number is one of the values that when multiplied by itself gives the original number. For instance, let's consider the number 9. We need to find the value of \(x\) such that \(x^2 = 9\).
To start, focus on the positive square root. This is typically what most people think of first when they hear 'square root'. For the number 9, the positive square root is found by calculating \( \sqrt{9} \), which equals 3.
Therefore, 3 is the positive square root of 9. Positive square roots are the non-negative solutions. In this context, non-negative means greater than or equal to zero.

In addition to the positive square root, every positive real number also has a negative square root. This isn't as well-known but is equally important.
Continuing with our example of 9, the negative square root can be found because both positive and negative numbers, when squared, result in a positive value. Thus, \(x^2 = 9\) has another solution: \(-x = -3\).
Therefore, -3 is the negative square root of 9. Even though it's a negative number, it still meets the criteria of squaring to give the original positive number. This is a crucial aspect of understanding square roots fully.

When solving equations involving square roots, it's essential to consider both the positive and negative roots. Let's go through the common steps in solving such equations:
* Identify the equation: Start with identifying the given equation, for example, \(x^2 = 9\).
* Find the square roots: Realize that you need to find both the positive and negative square roots. For \(x^2 = 9\), these are \(\sqrt{9} = 3\) and \(-\sqrt{9} = -3\).
* Check your work: Ensure that both solutions satisfy the original equation. Substituting back, we see that \(3^2 = 9\) and \((-3)^2 = 9\). Both are valid.
This demonstrates the importance of always considering both square roots when solving such equations to ensure all possible solutions are accounted for.