Estimate and place square roots and pi on a number line
Grade 8 Math Worksheet

Circle the best answer, or write your answer on the line.
Esme measures a diagonal that works out to √60. Between which two whole numbers is √60?
- 30 and 31
- 7 and 8
- 8 and 9
- 6 and 7
Luz rounds √44 to the nearest whole number. Which whole number is √44 closer to?
Use the picture in question 1.
- 6
- 7
- 6.5
Number line with a tick at every tenth. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Number line with a tick at every tenth. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. green: whole numbers blue: other integers orange: other rational numbers purple: irrational numbers -2 -1 0 1 2 Ren estimates √12 for a model. What is √12 to the nearest tenth?
Tala rounds √43 on a calculator. What is √43 to the nearest tenth?
Use the picture in question 3.
Zee finds √27 for a robot's path. What is √27 to the nearest tenth?
Use the picture in question 3.
Ari marks four points on a number line for a poster. Which point is closest to √18?
Number line with a tick at every tenth. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Point A is at 4.0, point B is at 4.2, point C is at 5.0, point D is at 9.0. Number line with a tick at every tenth. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Point A is at 4.0, point B is at 4.2, point C is at 5.0, point D is at 9.0. Green: whole numbers; blue: other integers; orange: other rational numbers; purple: irrational numbers 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9 A B C D - Point A
- Point B
- Point D
- Point C
Bo plots four points for a math club. Which point is closest to √26?
Number line with a tick at every tenth. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Point A is at 4.0, point B is at 5.0, point C is at 5.1, point D is at 6.0. Number line with a tick at every tenth. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Point A is at 4.0, point B is at 5.0, point C is at 5.1, point D is at 6.0. A B C D Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. - Point B
- Point C
- Point A
- Point D
Esme labels four points on a number line. Which point is closest to √47?
Number line with a tick at every tenth. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Point A is at 6.0, point B is at 6.5, point C is at 6.9, point D is at 7.0. Number line with a tick at every tenth. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Point A is at 6.0, point B is at 6.5, point C is at 6.9, point D is at 7.0. 6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7 A B C D Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. - Point D
- Point A
- Point C
- Point B
Kira subtracts a root from 9 on a worksheet. Between which two whole numbers is 9 − √45?
Number line with a tick at every whole number. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Squares to try: 6 × 6 = 36 and 7 × 7 = 49. Number line with a tick at every whole number. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Squares to try: 6 × 6 = 36 and 7 × 7 = 49. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Squares to try: 6 × 6 = 36 and 7 × 7 = 49. - 6 and 7
- 1 and 2
- 15 and 16
- 2 and 3
Luz subtracts a root from 12 in a puzzle. Between which two whole numbers is 12 − √70?
Number line with a tick at every whole number. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Squares to try: 8 × 8 = 64 and 9 × 9 = 81. Number line with a tick at every whole number. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Squares to try: 8 × 8 = 64 and 9 × 9 = 81. Number line with a tick at every whole number 0 10 20 30 40 50 60 70 80 90 100 Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Squares to try: 8 × 8 = 64 and 9 × 9 = 81. - 2 and 3
- 20 and 21
- 8 and 9
- 3 and 4