3.2 ­ Perfect Squares, Perfect Cubes, and their Roots 2017.notebook
February 15, 2017
Objectives:
­ Determine, using a variety of strategies, the square root of a perfect square.
­ Determine, using a variety of strategies, the cube root of a perfect cube.
­ Determine, concretely, whether given a whole number is a perfect square, perfect cube or neither.
­ Solve problems that involve square roots and cube roots.
Sep 8­3:41 PM
What is the area of each perfect square?
Why is the number a perfect square?
Feb 8­10:42 PM
1
3.2 ­ Perfect Squares, Perfect Cubes, and their Roots 2017.notebook
February 15, 2017
Steps to find the SQUARE ROOT of a number:
1. Determine the prime factorization without powers
2. Circle the PAIRS of common prime factors
3. Multiply one of each pair to get the square root.
Example 1
Determine the square root using prime factorization (without a calculator).
324
Sep 11­10:54 PM
You try:
Determine the square root using prime factorization (without a calculator).
1089 Sep 11­10:59 PM
2
3.2 ­ Perfect Squares, Perfect Cubes, and their Roots 2017.notebook
February 15, 2017
Perfect cube ­ any whole number that can be represented as the volume of a cube with a whole number edge length. Edge = Edge = Volume = Volume =
Edge = Edge = Volume =
Volume =
A perfect cube is a number that can be written as a power with an integer base and an exponent of 3. (i.e. volume of 27 units)
Cube root ­ is a number which when multiplied by itself 3 times results in a perfect cube value. (i.e. side length of 3 units)
What are some other examples of perfect cubes?
Sep 11­11:02 PM
Steps to find the CUBE ROOT of a number:
1. Determine the prime factorization without powers
2. Circle the TRIPLETS of common prime factors
3. Multiply one of each triplet to get the cube root.
Example 2
Determine the cube root using prime factorization (without a calculator).
1728
Sep 11­11:17 PM
3
3.2 ­ Perfect Squares, Perfect Cubes, and their Roots 2017.notebook
February 15, 2017
You try:
Determine the cube root using prime factorization (without a calculator).
2744
Sep 11­11:16 PM
Example 3
Determine the side length of the figure using prime factorization.
a)
b)
A = 676 m2
Sep 11­11:15 PM
4