3 2 Perfect Squares Perfect Cubes and Their

3. 2 Perfect Squares, Perfect Cubes, and Their Roots

WHAT IS THIS TOY CALLED?

Rubik’s Cube

What is the area of one face of the cube? Why is this number a perfect square? What is the volume of the cube? (This number is called a perfect cube) Why do you think it has this name?

What is a PERFECT SQUARE?

What is a PERFECT SQUARE? Any whole number that can be represented as the area of a square with a whole number side length PERFECT SQUARE is 25

What is the SQUARE ROOT? It is the side length of the square The SQUARE ROOT is √ 25 = 5 PERFECT SQUARE is 25

What is a PERFECT CUBE? Any whole number that can be represented as the volume of a cube with a whole number edge length PERFECT CUBE is 216

What is the CUBE ROOT? It is the edge length of the cube PERFECT CUBE is 216

Vocabulary

Determining the Square Root of 1296 • Write 1296 as a product of its prime factors (Prime Factorization): • Group the factors in pairs • Rearrange the factors in 2 equal groups 1296 = 2 • 2 • 3 • 3 • 3 = (2 • 2) • (3 • 3) = (2 • 3 • 3) • (3 • 2 • 2) = 36 • 36 The Square Root of 1296 is 36

Determining the Square Root of 1764 The Square Root of 1764 is 42

Determining the Cube Root of 1728 • Write 1728 as a product of its prime factors (Prime Factorization): • Group the factors in sets of three • Rearrange the factors in 3 equal groups 1728 = 2 • 2 • 2 • 3 • 3 = (2 • 2 • 2) • (3 • 3) = (2 • 2 • 3) • (2 • 3) = 12 • 12 The Cube Root of 1728 is 36

Determining the Cube Root of 2744 The Cube Root of 2744 is 14

A cube has volume 4913 cubic inches. What is the surface area of the cube? • Sketch a diagram • To calculate the surface area, first determine the edge length of the cube • The edge length e, of a cube is equal to the cube root of its volume • The surface area, SA, of a cube is the sum of the areas of its 6 congruent square faces.

A cube has volume 12 167 cubic inches. What is the surface area of the cube?

DO PROBLEMS Page: 146 -147 Problems: 4 - 10

HOMEWORK Page: 147 Problems: 13 -18

QUIZ Page: 149 Problems: 6 – 8, 10