1. 1.2 Multiply and Divide Radicals

2. I can multiply and divide radical expressions
Essential standard
I can multiply and divide radical expressions
I can rationalize the denominator

3. SIMPLIFY RADICALS EXPRESSIONS
1) 𝑥 ) 49 𝑥 ) 𝑥 10 𝑦 15

4. SIMPLIFY RADICALS EXPRESSIONS
4) ) 𝑎 3 𝑏 7
6) 54 𝑥 4 𝑦 5 𝑧 ) 60𝑥 𝑦 3

5. 𝑛 𝑥 ⋅ 𝑛 𝑦 = 𝑛 𝑥⋅𝑦 MULTIPLYING RADICALS
You can only multiply radicals with the same index.
𝑛 𝑥 ⋅ 𝑛 𝑦 = 𝑛 𝑥⋅𝑦

6. PROBLEM 1
Can you simplify the product of the radical expressions? Explain.
A) 3 6 ⋅ B) 3 −4 ⋅ 3 2

8. PROBLEM 2 What is the simplest form of 72 𝑥 3 𝑦 2 ⋅ 10𝑥 𝑦 3 ?
Reminder: 𝑛 𝑥 ⋅ 𝑛 𝑦 = 𝑛 𝑥⋅𝑦

10. DIVIDING RADICAL EXPRESSIONS
Much like multiplication, if two radicals have the same index you can divide the coefficients and divide the radicands. Then simplify.
𝑎⋅ 𝑛 𝑥 𝑏⋅ 𝑛 𝑦 = 𝑎 𝑏 ⋅ 𝑛 𝑥 𝑦

11. PROBLEM 3 What is the simplest form of the quotient?
A) 𝑥 𝑥 B) 𝑦 𝑦 2

13. RATIONALIZE THE DENOMINATOR
As long as you multiply a fraction’s numerator and denominator by the same number the value of the fraction does not change.
We can use this to ‘rationalize the denominator’.
→ ⋅ → 1⋅ ⋅ 2 →

14. PROBLEM 4
Simplify by rationalizing the denominator.
A.)

15. GOT IT?
Simplify by rationalizing the denominator.
7𝑥 5

16. I can multiply and divide radical expressions
Essential standard
I can multiply and divide radical expressions
I can rationalize the denominator