D. Adding and Subtracting Radicals

When adding and subtracting radicals, the radicals must be in simplest form and have 'like radicands' (identical radicands).

It's like having the same last name; once they match, addition and subtraction operations can occur.

For example, . Let's see how that can be?

Example 1 - Comparison

Adding radicals

Adding monomials

Example 2 - Comparison

Adding and subtracting radicals

Adding and subtracting monomials

Note: do not have the same exponent on the x and therefore cannot be further combined.

Note: A radical expression such as is in simplest form because the radicands are not the same.

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For further information about simplifying radical expressions see Example 3 on pp. 186 - 187 of Principles of Mathematics 11.