The document discusses operations on radicals, including simplifying radicals by identifying the index and radicand, and adding or subtracting radical expressions by combining like terms that have the same index and radicand. It provides examples of simplifying expressions involving addition and subtraction of radicals, emphasizing that unlike indices cannot be combined.

1. OPERATIONS ON
RADICALS

2. Mathematics Rewind

3. Give the index, radicand and
simplify the following
• 108
• 81
3
• 64
4
• 1
3
• 128
5

4. Adding and Subtracting
Radical Expressions

5. • Its really like adding or subtracting
like terms in simplifying algebraic
expressions, only this time, we need
the SAME INDEX AND RADICAND TO
SIMPLIFY.

6. STEP 1: SIMPLIFY THE
RADICAL IF POSSIBLE
• Example:
• 16
3
+ 54
3
+ 128
3
• = 2 2
3
+ 3 2
3
+ 4 2
3

7. STEP 2: ADD LIKE TERMS (IN
TERMS OF INDICES AND
RADICANDS)
• 2 2
3
+ 3 2
3
+ 4 2
3
=9 2
3
FINAL ANSWER: 9 2
3

8. Another example
• Simplify 72
3
+ 243
3
+ 8
3
• = 23 ∗ 9
3
+ 33 ∗ 9
3
+ 233
• =2 9
3
+ 3 9
3
+2
• = 2 + 5 9
3

9. REMEMBER!
• 𝐴 + 𝐵 ≠ 𝐴 + 𝐵
• If n and m are unequal, 𝑎𝑛
+ 𝑏
𝑚
≠
𝑎 + 𝑏
𝑚+𝑛

10. NOW YOU TRY
• ( 40
3
+ 625
3
)
• 7
4
+ 567
4
• 648
3
− 24
3