1. Rules and nth root Aug. 26 and 27
Simplifying Radicals
Rules and nth root
Aug. 26 and 27

2. Bell Ringer
Simplify:
3 18
25 ∙ 100
4 𝑡 6 𝑢 5 𝑣 4
8 𝑟 3 ∙ 9 𝑟 4

3. Homework!
Questions?
Correct odds.

4. Review: 12 63
108

5. Review
200 𝑚 4 𝑛
28 𝑥 3 𝑦 3
2 8 𝑝 2 𝑞 3 𝑟

8. Radical Rules
You can multiply two radicals if they have the same root:
𝑘 𝑟𝑜𝑜𝑡 𝑏𝑎𝑠𝑒 where 𝑘 is a constant
Ex. 5 × 8 = 40
Also seen as, 2 5 × 2 8 = 2 40
Ex ×2 6 =(3×2) 15×6 =6 90
Ex × 5 5 =

9. Radical Rules
You can add/subtract the constants in front of the radical if the roots AND the bases are the same.
𝑘 𝑟𝑜𝑜𝑡 𝑏𝑎𝑠𝑒 where 𝑘 is a constant
Ex: = =13 15
Sometimes you will need to simplify BEFORE you can add them together.
Ex: −2 8 − 18 − 24

10. Practice!
8 ×5 8
− −2 3
5 ∙− 15
48 ∙ 48

11. Radicals to the nth root
When taking radicals to the nth root, n is how many of a number need to be grouped together.
When we look at square roots, 2 𝑥 , we look for 2 of the same number to multiply to equal x.
Ex: 2 9 = 2 3×3 =3
So when we take 3 𝑦 , we look for a number multiplied by itself 3 times to equal y.
Ex: 3 8 = 3 2×2×2 =2

12. Practice!
3 27 𝑥 3
4 243 𝑠 4 𝑡
3 16 𝑥 4 𝑦 𝑧 5