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…√ …Perfect Squares...Square Roots…Roots…𝑥𝑥 2 …
The square root of all perfect squares will always be rational
A perfect square can NEVER be negative
o A perfect square is the PRODUCT of multiplying an integer by itself
However, a root can be negative or positive
o A root is the ANSWER to a square root problem
o It is the ACTUAL # being multiplied TO ITSELF
The fancy checkmark is a called a ‘radical’
o √9
 This is called “radical 9” OR “the square root of 9”
 9 is a perfect square
 The solution is ± 3
The “is it a perfect square?” SHORTCUT:
o EVEN amount of 0’s AND has a perfect square in the beginning
 900—perfect (9 is a perfect square and it has an even amount of 0’s)
 4,000—NOT PERFECT (4 is a perfect square BUT IT IS AN ODD AMOUNT OF 0’s)
Remember:
o A perfect SQUARE will NEVER be a NEGATIVE
o The square root of a perfect square is rational (Q)
 √# --- # comes from the ‘Perfect Square’ column below
o The square root of any whole number that is NOT a perfect square is IRRATIONAL (I)
 √# --- # is not from the perfect square column (it’s in-between 2 perfect squares)
Root
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
20
25
30
Root Squared 𝑥𝑥 2 Square Root √
12 =1
22 =4
32 =9
42 =16
52 =25
62 =36
72 =49
82 =64
92 =81
102 =100
112 =121
122 =144
132 =169
142 =196
152 =225
202 =400
252 =625
302 =900
√1=±1
√4=±2
√9=±3
√16=±4
√25=±5
√36=±6
√49=±7
√64 =±8
√81=±9
√100=±10
√121=±11
√144=±12
√169=±13
√196=±14
√225=±15
√400=±20
√625=±25
√900=±30
Perfect Square
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
400
625
900