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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