Aim: How do we multiply or divide radical expressions?

35325

xx

525

Do Now: 1. Multiply:

2. Multiply:

3. Divide:

4. Divide:

xx 32

5352

HW: p.97 # 6, 8, 10, 15, 19, 20, 22, 24

To multiply or divide radicals, we do it just like multiply or divide polynomials, and then we need to simplify if applicable.We cannot combine 2x + 2y or 2x – 2y, but we can do 2x ∙ 2y or 2x ÷ 2y Therefore, we can multiply or divide radicals with same or different radicands, but the indices must be the same

is OK but 2

is OK but 25

For instance:

3 3 3

2 10 5220

6 12

Multiply then simplify

72 36 2 6 2 =

More examples

4√24 𝑥3 ∙2√3 𝑥¿8 √72 𝑥4¿8 ∙6 𝑥2 √2

4√ 48𝑥2 ∙ 4√ 𝑥2

3¿ 4√ 48𝑥2 ∙ 𝑥

2

3= ¿ 4

28

28

24

327

3125448 3125448

3

544 184

234 212

170 17

28

28

24

327

3125448 3125448

3

544 184

234 212

170 17

3

3 4

232xx

3

3

242xxx

34xxx x3 4

3327 xx

3

5

15

45

x

x

xyxyyx

541581012 323

¿√ 27 𝑥3 𝑥3¿√ 9

𝑥2¿

3𝑥

¿√ 45 𝑥5

15 𝑥3 ¿√3 𝑥2¿ 𝑥√3

¿3 √ 10 𝑥3 𝑦 2

5𝑥𝑦 −2√ 15 𝑥 𝑦2

5𝑥𝑦¿3 𝑥 √2 𝑦−2√3 𝑦

85123

9453

3 2

3 5

2550x

x

xx

103402 3

𝟔𝟎√𝟔

𝟑𝟔√𝟓

𝒙 𝟑√𝟐

𝟐𝟑 √𝟒 𝒙𝟐=

𝟐𝟑 ∙𝟐𝒙=

𝟒 𝒙𝟑