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3.2 _________________________________________________ Determine the side lengths of the following squares. Diagrams are not to scale. Hints: How is the area of a square determined? What is true about the sides of a square? A = 100 cm2 A = 49 cm2 A = 196 cm2 The side of a square is the______________ ______________ of the area. The squares above have side lengths that are whole numbers. If the side of the square is a whole number then the area is a ____________ _____________ . Which of the following are perfect squares? i) 144 ii) 50 iii) 2500 Suggest 2 more perfect squares. Explain why 14 is not a perfect square. The square root symbol is iv) 999 Determine the edge lengths of the following cubes. Diagrams are not to scale. Hints: How do you determine the volume of a rectangular prism? What is true about the sides of a cube? V = 1000 m3 V = 125 m3 V = 8 m3 The edge of a cube is the______________ ______________ of the volume. The cubes above have edge lengths that are whole numbers. If the edge of the cube is a whole number then the volume is a ____________ _____________ . Which of the following are perfect cubes? i) 27 ii) 216 iii) 9 Suggest 2 more perfect cubes. 3 The symbol for cube root is iv) 999 Determining Square Roots and Cube Roots of Perfect Squares and Perfect Cubes Prime factorization can be used to determine square roots and cube roots of perfect squares and perfect cubes. Determine the prime factorization of 324. Any combination of the prime factors would also be a factor. Can the factors be arranged into 2 identical groups? Those identical groups would suggest 2 identical #s that would multiply to equal 324 (i.e. the square root of 324). Given that 16875 = 54 x 33, explain why 16875 is not a perfect square. Try using prime factorization to determine the cube root of 3375. How will the procedure differ from finding a square root?