Math 10 Unit 2: Roots and Powers (Day 1) Name:

Intro to Number Systems; Square Roots and Cube Roots

Learning Intention(s):

Introduction to number systems Review square and cube roots

Number Systems: Natural Numbers: Whole Numbers: Integers:

Rational Numbers: Any number that can be written as a fraction, m

n this includes terminating and

repeating decimals.

Irrational Numbers: Any number that is not rational; it cannot be written in the form m

n. where m and n

are integers, n ≠ 0 Ex: Determine the sets the following belong:

16 =_________

21 =_________

5.3 =_________

6.2 =_________

49 =________ =_________

Review: Square Roots and Cube Roots

When a number x can be written as the product of two equal factors, then the square root of x,

represented by ,x is one of these factors.

For example, 64 8 because 82 = 64.

8 is a square root of 64

We write 8=√64

Note: The square root of a perfect square is always a rational number.

The cube root of a number x, represented by 3 ,x is one of three equal factors of the number.

For example, 3 64 4 because 43 = 64.

4 is a cube root of 64

We write 4= √64 3

Note: The cube root of a perfect cube is always a rational number.

So, how would you write 6 as a square root? A cube root? A fourth root?

We call the form √xn a radical. *When evaluating a radical, you can use groupings of prime factors to calculate square roots of perfect squares and cube roots of perfect cubes.

256 2 2 2 2 2 2 2 2

3 3125 5 5 5

Homework: 1.1 # 1-6 1.3 # 1-4even (calculator okay)