1. Multiplying, Dividing, Adding & Subtracting Radicals
Unit 6.3
Multiplying, Dividing, Adding & Subtracting Radicals

2. When adding or subtracting radicals, the root indices must be the same, and the radicands (the numbers underneath the radical symbols) must also be the same. Sometimes, it is necessary to simplify radicals before they can be combined.
Example 1. Add or Subtract, simplify your answers.
Think about combining like terms in the expression: 2𝑥+5𝑦+3𝑥. What can you combine and what would your simplified expression be?
Radical expressions work the same way, you need like terms to add or subtract!
A − B − − C. 𝑥 3 16𝑥 − 3 54 𝑥 4

3. Think about if you were given the multiplication problem 3𝑥𝑦∙2𝑥 What would your answer be? Radicals work the same way; you can multiply without like terms.
Example 2. Multiply and simplify your answers.
A ∙ B. 𝑥 3 6𝑥 ∙3 3 8 𝑥 2   
C (5 2 −7 3 ) D

4. You do not need like terms to divide
You do not need like terms to divide. It is easier to divide and THEN simplify the radical, but you can actually do it either way.
Example 3. Divide and simplify your answers
A 𝑎 𝑏 𝑎𝑏 B 𝑥 4 𝑦 2 𝑥 2

5. Occasionally, it is necessary to remove radicals from denominators of fractions. This process is called rationalizing. If the denominator contains a binomial containing one or more radicals, you should multiply by the conjugate of the denominator Reminder: the conjugate of 5 − is
Example 4. Rationalize the denominators.
A B  C