Introduction to Radicals
Overview of Objectives, students should be able to:
1. 2. 3. 4. Find square roots Approximate square roots Find cube roots Simplify radical containing variables
Main Underlying Questions: 1. How do you find square and cube roots?
2. How do you simplify radical expressions containing variables? 3. What is the relationship between exponents and roots?
Objectives:
• Find square roots
Activities and Questions to ask students: • What is 5 2 ? What is 6 2 ?
• • • Tell students the process of “undoing” a square is called the square root, symbolized by What is another way to explain the process of taking the square root? What is 25 ? What is 36 ? What is 50 ? Is there a way to approximate the number? Tell students the cube root is symbolized by 3
• •
Approximate square roots Find cube root
• • • • • • •
Discuss the parts of the radical using terminology: index radicand Give examples of higher order radicals and ask students what relationship they see between the index and the type of the root. If the square root is the process of “undoing” a square root, what does the cube root do? What is another way to explain the process of taking the cube root? What is 3 8 ? What is 3 64 ? What is 9 ? What is 3 2 ? Have students work several examples like this. Have students draw the conclusion that a 2 = a Remind students to think about what the process of the square root is. What if we have numbers and variables 9a 2 ? What is 3 4 = 81 = 9 ? Have students then write 9 as a power of 3: 32 Have students work several examples to show that a n = a
n
2
•
Simplify radical containing variables
• • • • • •
90
12/4/08