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Lesson 4 Math 1201 Perfect Squares, Perfect Cubes, and Their Roots In Grade 8, perfect square numbers were connected to the area of squares. When determining the square root of a whole number, we can envision a square as the perfect square number, and either side length as the square root. For example, a square with side length 3 has an area of 9 tiles. 3 9 3 or 32 9 3 Students can use a variety of strategies to determine the square root of a perfect square. If a number is the product of two equal factors or if the factors can be grouped in equivalent sets, the number is a perfect square. For example, 324 is a perfect square since it can be rewritten as 2 3 3 2 3 3, therefore the value of 324 2 3 3 2 3 3 2 3 3 18 . Another method involves whether a number has an odd or even number of factors. If a number has an odd number of factors, the number is a perfect square. When the factors are listed in order, the middle factor is defined to be the square root. For example, 36 has the factors 1,2,3,4,6,9,12,18 and 36. There are 9 factors, which is an odd number. Therefore, 36 is a perfect square and 6, the middle factor, is the square root. When determining the cube root of a whole number, students should view the perfect cube number as the volume and cube root as any one of the three equivalent dimensions. For example, a cube with side length 4 cm has a volume of 64 cm3. We can verify the value of the volume using the formula V l w h . New notation, 3 64 4 , means the cube(third) root of sixty four is equal to four. index is a way to determine what root the questions is referring. For example, so on. 4 represents the fourth root, 5 represents the sixth root and represents square root and the index of 2 is implied and not written. Student can use prime factorization to determine the cube root of number. For example, 3 216 3 2 3 2 3 2 3 6 Worksheet Math 1201 Name:___________ 1. List the factors of 256. Use the factors to determine the square root of 256. 2. If 1000 cubes were combined to make a giant cube, what is the area of each face? 3. Simplify the following: A) 3 B) C) 343 121 3 216 3 64 3 1000 25