# Download 3.2 Determine the side lengths of the following squares. Diagrams

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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?
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