# Packet Roots and Pythagorean Theorem

```Name___________________________ Period___ 8R 13.2 Perfect Squares and Cubes CLASS WORK
Perfect Squares and Perfect Cubes
Vocabulary:
• Perfect square- the answer to a number multiplied by itself two times.
• Square root- the number that when multiplied by itself is equal to the given number.
• Perfect cube- the answer to a number multiplied by itself three times.
• Cube root- a number that when raised to the third power is equal to the given number.
Part 1: Perfect Squares
List the first 15 perfect squares:
____ , ____ ,_____ , ____ , ____ , ____ ,_____ , ____ ,_____ , ____ ,_____ ,_____ , ____ ,_____ ,_____
12
22
32
42
52
62
72
82
92
102
112
122 132
142
152
Examples: Simplify
1) √36 = ________ because (
3) &plusmn;√. 09 = ________
2) −√64 = ________
)2 is 36
4)
5) −
= ________
√
= ________
√
Part 2: Perfect Cubes
List the first 10 perfect cubes:
_____ , _____ , _____ , _____ , _____ , _____ , _____ , _____ , _____ , _____
13
23
33
43
53
63
73
83
93
103
Examples: Simplify
6) √27 = ________ because (
)3 is 27
8) &plusmn; √125 = ________
9)
7) − √8 = ________
10) −
= ________
√
√
= ________
Part 3: Equations: Solve each equation for x
Examples:
11)
= 81
2)
= 1000
3) = 1.44
4)
= 121
5)
= 512
Try These:
1) √9
2) −√100
4)
5)
7)
= 36
√
6) √4 + 5
√
8)
3) &plusmn;√. 0004
=1
= 144
9)
10) The area of a square boxing ring is 225ft2. What is the length of one side? (a = s2)
11) √125
12) − √64
13)
14) − √216
15)
16)
17) 18)
=.064
= 1000
20) The volume of a cube is 125 ft3. What is the length of one side? ( v = s3)
√1
√
√
19) x3 =
```