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Square roots are all about finding a number which, when multiplied by itself, gives the original number we started with. For instance, when you think of the square root of 400, you’re looking for a number that when squared (multiplied by itself) results in 400. Calculating square roots can sometimes feel tricky, but with practice, it becomes easier.
The process involves identifying that one number which produces the perfect square. In the case of 400, it turns out that 20 multiplied by 20 equals 400. Therefore, the square root of 400 is 20. This discovery not only helps in finding the value but also in understanding the structure behind numbers. It's a neat way of breaking things down to smaller, easily manageable parts.

Classifying numbers involves understanding the nature of numbers and how they relate to each other. When we talk about classes of numbers, we break them down into categories such as whole numbers, fractions, mixed numbers, and so on. However, the most common classification we often use is distinguishing between rational and irrational numbers.

Here’s what makes a number rational:

• A number is rational if it can be written as a fraction, where both the numerator and the denominator are integers.
• It must have a finite or a repeating decimal expansion.

In the previous step, we found that the square root of 400 is 20. Since 20 can be expressed as \( \frac{20}{1} \), it is clearly a rational number. This classification method is crucial in understanding number properties.

Irrational numbers are quite unique; they cannot be written as simple fractions. These numbers have decimal expansions that go on forever without repeating. This is what makes them different from rational numbers.Imagine trying to find a fraction for numbers like \( \pi \) (pi) or the square root of numbers like 2 and 3 - you simply can’t do it. They maintain a certain level of 'chaos' in their decimal expansions.To grasp this concept, let’s remember:

• Irrational numbers can’t be neatly expressed as a fraction.
• Their decimal form is endless and non-repeating.

Understanding the difference between rational and irrational numbers helps in simplifying and solving problems related to square roots and other number classifications. It makes it easier to see why something like the square root of 400 is rational due to its clear whole number outcome, unlike the perplexing nature of many other roots or constants.