Exploring Adding and Multiplying Radicals

What is the main goal of today's lesson?

• To understand operations with radical functions

• To learn about polynomial functions

• To explore trigonometric identities

• To study linear equations

When simplifying the square root of 20, what is the leftover inside the radical?

• 10

• 2

• 3

• 5

How do you combine 3√20, -√45, and 4√80 after simplifying them?

• By adding the coefficients directly

• By multiplying all terms

• By subtracting the smallest term from the largest

• By finding like radicals and then combining

What must be true for radicals to be combined through addition or subtraction?

• They must be prime numbers

• They must have the same coefficient

• They must be like radicals with the same root

• They must be different types of roots

What is the result of multiplying 2√5 and 3√7?

• 5√35

• 10√35

• 6√35

• 6√12

Why can't you combine a square root with a cubed root?

• Because they are both irrational numbers

• Because they are both prime numbers

• Because they have different coefficients

• Because they are not like radicals

What is the simplified form of 2√3 * 4√5?

• 6√8

• 8√8

• 6√15

• 8√15

When distributing √7 to 3√2 + 2√7, what is the result?

• 3√14 + 2√49

• 3√14 + 2√21

• 3√14 + 2√7

• 3√14 + 2√14

What is the result of distributing 3√2 to 4 + √5?

• 12√2 + 3√10

• 12 + 3√10

• 12√2 + 3√5

• 12 + 3√5

What is the final simplified form of 3√2 * (4 + √5)?

• 12 + 3√5

• 12 + 3√10

• 12√2 + 3√5

• 12√2 + 3√10