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A square root is a value that, when multiplied by itself, gives the original number. For instance, the square root of 9 is 3 because 3 * 3 = 9. We use the radical symbol, \(\sqrt{}\), to denote the square root. To simplify a square root, like \(\sqrt{8}\), you need to break the number inside the radical down into its prime factors and find perfect squares. In this case, we rewrite 8 as 4 * 2, where 4 is a perfect square. This allows us to simplify \(\sqrt{8}\) as \(\sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}\).
Note that the square root of a number that is a perfect square is always a whole number. For example, \(\sqrt{16} = 4\) because 4 is the number which when squared gives 16.

Perfect squares are numbers that have an integer square root. These are very useful when simplifying square roots. Examples include 1, 4, 9, 16, 25, etc. Any time you can express a number inside a square root as a product of a perfect square and another integer, it simplifies the problem. For instance, in the expression \(\sqrt{8}\), we identified 4 as a perfect square because \(4 = 2^2\). This allowed us to rewrite \(\sqrt{8}\) as \(2\sqrt{2}\).
Always look for the largest perfect square factor to make simplification easier. In our exercise, we also simplified \(\sqrt{28}\) by identifying 4 as a factor, resulting in \(2\sqrt{7}\).

In algebra, like terms are terms whose variables and their exponents are the same. When simplifying expressions involving radicals, you can only combine like terms. For example, \(2\sqrt{2} & 2\sqrt{2}\) are like terms and can be combined, but \(2\sqrt{2}\) and \(2\sqrt{7}\) are not because the numbers inside the radicals are different.
In the given problem, we ended up with ‎‎\(2\sqrt{2} + 2\sqrt{7}\). Since these are not like terms, we cannot simplify the expression any further. Combining like terms helps to streamline expressions and solve equations more efficiently.