Section 6.3
Adding and Subtracting Radical Expressions
Recall adding and subtracting like terms
2𝑥 + 5𝑥 2 − 6𝑥 + 𝑥 2
To add or subtract radical terms,
1. Simplify each radical. Whatever comes out get multiplied by what is already out front.
(You should still have the same number of terms that you started with.)
2. Combine like terms. Keep the same variable/radical portion, add/subtract the constants.
(Like terms: After the constant, variables AND radicals must match exactly.)
Example 1: Combine the following expressions.
4√2 + 3√2 − √2
a)
5
5
5
b)
5
5
c) 3√5 − 7𝑥 √5 + 2√5 − 3𝑥 √5 − 3𝑥 2 √5
d)
4√2 + 3𝑥 √2 − √2
−√40
−
√90
−
√160
f)
h)
3
3
√250𝑥𝑦 2 −
4
√54𝑥𝑦 2
4
g)
4
5𝑥 √3𝑦5 + 𝑦 √243𝑥4 𝑦 + √48𝑥4 𝑦5
5𝑎2 √27𝑎𝑏 3
−
6𝑏 √12𝑎5 𝑏