Download notes

Pin the Irrational Tail on the Number Line
Directions: Use your knowledge of perfect squares to determine rational number approximations for the irrational
numbers listed in the first column. Then show the approximate location of each number on the number line. The
first one is done for you. Use the perfect squares worksheet to help you with the rationale.
− √24
-5
Irrational
Number
√𝟏𝟖
√𝟑
−√𝟐
−√𝟐𝟒
√𝟏𝟐
√𝟕
−√𝟓
− √𝟏0
-4
-3
− √5
− √2
-2
√3
-1
0
1
√7
2
√12 √15 √𝟏𝟖
4
3
5
Reasoning Process
Value
Rational
Approximation
18 is between the perfect squares 16 and 25 but closer to 16.
√18 is between 4 and 5 but closer to 4 on the number line.
3 is between the perfect squares 1 and 4 but closer to 4. √3 is
between 1 and 2 but closer to 2 on the number line.
2 is between the perfect squares 1 and 4 but closer to 1. −√2 is
between -1 and -2 but closer to -1 on the number line.
24 is between the perfect squares 16 and 25 but closer to 25.
−√25 is between -4 and -5 but closer to -5 on the number line.
12 is between the perfect squares 9 and 16 but closer to 9. √12
is between 3 and 4 but closer to 3 on the number line.
7 is between the perfect squares 4 and 9 but closer to 9. √7 is
between 2 and 3 but closer to 3 on the number line.
5 is between the perfect squares 4 and 9 but closer to 4. −√5 is
between -2 and -3 but closer to -2 on the number line.
4.242640687…
4.243
1.732050807…
-1.414213562…
-4.898979485…
3.464101615…
2.645751311…
-2.236067977…
(to the nearest
thousandths)
1.732
-1.414
-4.899
3.464
2.646
-2.236
−√𝟏𝟎
√𝟏𝟓
10 is between the perfect squares 9 and 16 but closer to 9.
−√10 is between -3 and -4 but closer to -3 on the number line.
15 is between the perfect squares 9 and 16 but closer to 16. √15
is between 3 and 4 but closer to 4 on the number line.
-3.162277660…
3.872983346…
-3.162
3.873