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

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

Homework! Questions? Correct odds.

Review: 12 63 108

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

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. 3 15 ×2 6 =(3×2) 15×6 =6 90 Ex. 3 23 × 5 5 = 3 23 5 5

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: 5 15 +8 15 = 5+8 15 =13 15 Sometimes you will need to simplify BEFORE you can add them together. Ex: −2 8 − 18 − 24

Practice! 8 ×5 8 −3 27 +4 27 −2 3 5 ∙− 15 48 ∙ 48

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

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