Don’t be Irrational
VOCABULARY
Square root - A number when multiplied by itself gives the original number. For example:
4 x 4 = 16 so the square root of 16 is 4. √16 = 4.
Perfect square - A number that has a rational number as its square root. For example:
100 is a perfect square because 10 x 10 = 100. 102 is not a perfect square because its
root is 10.09950493836208…. (an irrational number).
Irrational number - A real number that can be written as a non-repeating, non-terminating
decimal, but NOT as a fraction (√3, π, √10).
RULES:
1.
Place all game pieces (erasers) on the “pi” space.
2. Player A rolls the die and moves his/her eraser the correct number of spaces to land on an
irrational number. He/she then:
a.
Writes this irrational number on the back of this page.
b. Writes the 2 numbers that the irrational number is between.
c.
Circles the number that the irrational number is closest to.
d. Writes a decimal approximation for the irrational number.
3. A student checks Player A’s work with a calculator to determine if he/she gave the correct
answer.
4. A player can earn a point (for a maximum of 2 points/turn). Points are awarded as follows:

One point for correctly writing down the two integers the irrational number
lies between.

One point for correctly circling the integer that is closest to the irrational
number.
5. Repeat #2-4 for Player B, etc.
6. Tally the points at the end of the game to determine the winner.
Perfect Squares from 1 – 15
Directions: Fill in all the blanks to complete the table. The first 2 entries are done
for you.
Volunteer Note: On the Student Version the BLUE UNDERLINED numbers
are blank.
Perfect Squares
Square Root
12 = 1 x 1 = 1
√1 = 1
22 = 2 x 2 = 4
√4 = 2
32 = 3 x 3 = 9
√ 9 = 81
42 = 4 x 4 = 16
√ 16 = 4
52 = 5 x 5 = 25
√25 = 5
62 = 6 x 6 = 36
√ 36 = 6
72 = 7 x 7 = 49
√ 49 = 7
82 = 8 x 8 =64
√64 = 8
92 = 9 x 9 = 81
√ 81 = 9
102 = 10 x 10 = 100
√ 100
= 10
112 = 11 x 11 = 121
√ 121
= 11
122 = 12 x 12 =144
√ 144 = 12
132 = 13 x 13 = 169
√ 169
= 13
142 = 14 x 14 = 196 √ 196
= 14
152 = 15 x 15 = 225
= 15
√ 225
Write what a rational number
is and provide 2 examples.
Student Recoding Sheet
√
√ lies
Decimal
Calculator
between
Approximation
Check
Points
1. √2
between 1 and 2
24. √150 between 12 and 13
2. √6
between 2 and 3
25. √156 between 12 and 13
3. √7
between 2 and 3
26. √175
between 13 and 14
4. √13
between 3 and 4
27. √176
between 13 and 14
5. √15
between 3 and 4
28. √190
between 13 and 14
6. √18
between 4 and 5
29. √192
between 13 and 14
7. √22
between 4 and 5
30. √200
between 14 and 15
8. √23
between 4 and 5
31. √216
between 14 and 15
9. √31
between 5 and 6
32. √240
between 15 and 16
10.
√32
between 5 and 6
33. √245
between 15 and 16
11.
√40
between 6 and 7
34. √250
between 15 and 16
12.
√65
between 6 and 7
35. √269
between 16 and 17
13.
√56
between 7 and 8
36. √275
between 16 and 17
14.
√65
between 8 and 9
37. √287
between 16 and 17
15.
√68
between 8 and 9
38. √300
between 17 and 18
16.
√75
between 8 and 9
39. √316
between 17 and 18
17.
√84
between 9 and 10
40. √325
between 18 and 19
18.
√96
between 9 and 10
41. √360
between 18 and 19
19.
√98
between 9 and 10
42. √363
between 19 and 20
20.
√108
between 10 and 11
43. √388
between 19 and 20
21.
√132
between 11 and 12
44. √412
between 20 and 21
22.
√135
between 11 and 12
45. √630
between 25 and 26
23.
√148
between 12 and 13
 If students need to visualize which numbers the square root is between, encourage them to draw
a number line and think about which of the two numbers the square root is closer to.
√2
√190
√190