# 3.2 Square Roots and Cube Roots

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```FCP 10
3.2 Square Roots and Cube Roots
Study the table below of perfect squares and perfect cubes. What patterns do you
observe?
Perfect Prime
Squares Factorization
1
Square
Root
1 1
Perfect
Cubes
Prime Factorization
1
Cube Root
3
1
1
2
4
2x2
4
2
8
2x2x2
3
8
9
3x3
9
3
27
3x3x3
3
27
3
16
2x2x2x2
16
4
64
2x2x2x2x2x2
3
64
4
25
5x5
25
5
125
5x5x5
3
125
5
36
2x2x3x3
36
6
216
2x2x2x3x3x3
3
216
6
100
2x2x5x5
100
10
1000
2x2x2x5x5x5
3
1000
10
144
2x2x2x2x3x3
144
12
1728
2x2x2x2x2x2x3x3x3
3
1728
12
49
Thus
And
3
729
______ because ____________
________ because ____________
A perfect square is the product of _________ equal _______________
A perfect cube is the product of __________ equal ________________
How can prime factorization be used to determine if a number is a perfect square?
How can prime factorization be used to determine if a number is a perfect cube?
Notice that some numbers are both perfect squares and perfect cubes (1 and 8)
1. Which of the following numbers is a perfect square? A perfect cube? Neither?
a) 512
b) 300
c) 729
Prime Factorization
a) 512
b) 300
c) 729
300
729
Calculator
512
3
512
3
300
3
729
2. Determine the answers to the following: (Use a calculator only when appropriate)
a)
4
2
b)
d)
5
e)
g)
25x 2
h)
3
4
3
5
3
3
16 25
c)
32
f)
27
81
i)
36
25
j)
m)
3
27
8
k)
3
6
8
n)
3
3
27 125
27d 3
l)
o)
3
125x 3
3
27 000
3. The volume of a cube is 512 in3. What is the surface area of the cube?
4. The surface area of a sugar cube is 13.5 cm2. What is the volume of the cube?
```