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Radical expressions include numbers under the symbol of a square root, cube root, or higher roots. For instance, the expression \( \sqrt{20} \) from the exercise is a square root, which is a type of radical. Simplifying radicals involves breaking down the number inside the root into its prime factors and then simplifying it by taking out the square root of any perfect squares that are present.

To make these expressions easier to work with, we often try to express them in the simplest form possible. By doing this, operations such as addition, subtraction, multiplication, and division with radical expressions become more manageable. A handy trick to remember is that the square root of a product \( \sqrt{ab} \) is equal to the product of the square roots \( \sqrt{a} \cdot \sqrt{b} \) as shown in the exercise with \( \sqrt{20} = \sqrt{4 \cdot 5} \) which simplifies to \( 2\sqrt{5} \).

In algebra, like terms are terms that have the same variable raised to the same power. However, when dealing with radical expressions, like terms are those that have the same radical part - that is, the same number under the root. For example, in the terms \( 2\sqrt{5} \) and \( 6\sqrt{5} \) derived from the exercise, the \( \sqrt{5} \) part is the same, making these terms 'like terms'.

To combine like terms, we simply add or subtract the coefficients (numbers in front of the radicals) while keeping the radical part unchanged. This is analogous to adding quantities of the same unit; just as you would combine '2 apples' with '5 apples' to make '7 apples', you combine \( 2\sqrt{5} \) with \( 6\sqrt{5} \) to get \( 8\sqrt{5} \).

Adding radicals can only be done when the radicals in question are like terms. This is similar to the concept of combining like terms as previously discussed. When adding square roots, such as \( \sqrt{a} \) and \( \sqrt{b} \), they must have the same radicand (the number under the root) to be added directly.

For the problem at hand, once the radicals have been simplified and identified as like terms, as in the step from \( \sqrt{20} \) being simplified to \( 2\sqrt{5} \), we can simply add the coefficient of \( 2\sqrt{5} \) to that of \( 6\sqrt{5} \) to find the result, which in this case is \( 8\sqrt{5} \). Remember that the radical part does not change during the addition unless it can be further simplified. This process closely resembles adding simple algebraic terms with the same variable and exponent.