1. 7.3 – Multiplying and Simplifying Radical Expressions
Math 71B
7.3 – Multiplying and Simplifying Radical Expressions

2. Product Rule for Radicals
𝑛 𝑎 ⋅ 𝑛 𝑏 = 𝑛 𝑎𝑏
(Disclaimer: Only works when 𝑛 𝑎 , 𝑛 𝑏 are real #s. Some restrictions apply. See stores for details.)

3. Product Rule for Radicals
Ex 1. Multiply: 3 7 ⋅ 3 9 = 𝟑 𝟔𝟑 𝑥+2 ⋅ 𝑥−2 = 𝒙+𝟐 𝒙−𝟐

4. Product Rule for Radicals
Ex 1. Multiply: 3 7 ⋅ 3 9 = 𝟑 𝟔𝟑 𝑥+2 ⋅ 𝑥−2 = 𝒙+𝟐 𝒙−𝟐

5. Product Rule for Radicals
Ex 1. Multiply: 3 7 ⋅ 3 9 = 𝟑 𝟔𝟑 𝑥+2 ⋅ 𝑥−2 = 𝒙+𝟐 𝒙−𝟐

6. Simplifying Radicals
4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, … are ___________________ (squares of integers) 8, 27, 64, 125, 216, 343, … are ______________ 16, 81, 256, 625, … are ____________________

7. Simplifying Radicals
4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, … are ___________________ (squares of integers) 8, 27, 64, 125, 216, 343, … are ______________ 16, 81, 256, 625, … are ____________________
perfect squares

8. Simplifying Radicals
4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, … are ___________________ (squares of integers) 8, 27, 64, 125, 216, 343, … are ______________ 16, 81, 256, 625, … are ____________________
perfect squares
perfect cubes

9. Simplifying Radicals
4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, … are ___________________ (squares of integers) 8, 27, 64, 125, 216, 343, … are ______________ 16, 81, 256, 625, … are ____________________
perfect squares
perfect cubes
perfect fourth powers

10. Simplifying Radicals
Ex 2. Simplify: 80 = 3 40 = 200 𝑥 2 𝑦 = 3 𝑥 2 −12𝑥+12 =

11. Simplifying Radicals
Recall: If 𝑛 is even, 𝑛 𝑎 𝑛 =|𝑎|. If 𝑛 is odd, 𝑛 𝑎 𝑛 =𝑎. Note: If 𝑎 is nonnegative, then the first rule becomes 𝑛 𝑎 𝑛 = _____.

12. 𝒂 Simplifying Radicals
Recall: If 𝑛 is even, 𝑛 𝑎 𝑛 =|𝑎|. If 𝑛 is odd, 𝑛 𝑎 𝑛 =𝑎. Note: If 𝑎 is nonnegative, then the first rule becomes 𝑛 𝑎 𝑛 = _____. 𝒂

13. Simplifying Radicals
Ex 3. Simplify (assume that all variables are positive real numbers). 𝑥 6 = 𝑥 7 𝑦 11 𝑧 3 = 3 40 𝑥 10 𝑦 14 = 5 32 𝑥 12 𝑦 2 𝑧 8 =

14. Simplifying Radicals
Ex 4. Multiply and simplify (assume that all variables are positive real numbers): 6 ⋅ 2 = ⋅5 3 2 = 4 4 𝑥 2 𝑦 ⋅ 4 8 𝑥 6 𝑦 3 =