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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 464 · 40 questions
TalentJR

How to do it in your head (Guess, divide, average): Division: round the divisor to the nearest ten and find the closest multiple of it. Square root: guess the nearest whole root, then divide the number by your guess. Average the guess and the answer of the division, and round to 1 decimal place.

NameDateTime takenScore ___ / 40
  1. 1.√37 to 1 decimal place? (a) 6.4 (b) 6.2 (c) 6.1 (d) 6.3
  2. 2.Best estimate of 1066 ÷ 51? (a) 21 (b) 210 (c) 2100
  3. 3.√80 to 1 decimal place? (a) 8.8 (b) 9.0 (c) 8.7 (d) 8.9
  4. 4.√92 to 1 decimal place? (a) 9.6 (b) 9.5 (c) 9.3 (d) 9.4
  5. 5.√61 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 7.6 (d) 7.9
  6. 6.Best estimate of 3344 ÷ 52? (a) 67 (b) 6700 (c) 670
  7. 7.Best estimate of 1723 ÷ 83? (a) 22 (b) 220 (c) 2200
  8. 8.√66 to 1 decimal place? (a) 8.0 (b) 8.3 (c) 8.2 (d) 8.1
  9. 9.Best estimate of 1598 ÷ 57? (a) 270 (b) 2700 (c) 27
  10. 10.√74 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.6 (d) 8.7
  11. 11.Best estimate of 5026 ÷ 68? (a) 720 (b) 7200 (c) 72
  12. 12.Best estimate of 3605 ÷ 48? (a) 7200 (b) 720 (c) 72
  13. 13.Best estimate of 1272 ÷ 34? (a) 42 (b) 420 (c) 4200
  14. 14.Best estimate of 1961 ÷ 86? (a) 2200 (b) 22 (c) 220
  15. 15.√65 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.3 (d) 8.4
  16. 16.√32 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.6 (d) 5.7
  17. 17.Best estimate of 2837 ÷ 49? (a) 5700 (b) 57 (c) 570
  18. 18.√29 to 1 decimal place? (a) 5.4 (b) 5.7 (c) 5.5 (d) 5.6
  19. 19.Best estimate of 1637 ÷ 32? (a) 5500 (b) 550 (c) 55
  20. 20.√72 to 1 decimal place? (a) 8.6 (b) 8.4 (c) 8.5 (d) 8.7
  21. 21.Best estimate of 984 ÷ 48? (a) 200 (b) 20 (c) 2000
  22. 22.Best estimate of 3704 ÷ 66? (a) 530 (b) 5300 (c) 53
  23. 23.Best estimate of 668 ÷ 51? (a) 1300 (b) 13 (c) 130
  24. 24.Best estimate of 3574 ÷ 58? (a) 6000 (b) 60 (c) 600
  25. 25.√45 to 1 decimal place? (a) 6.8 (b) 6.6 (c) 6.7 (d) 6.9
  26. 26.Best estimate of 3420 ÷ 46? (a) 68 (b) 680 (c) 6800
  27. 27.Best estimate of 845 ÷ 48? (a) 1700 (b) 17 (c) 170
  28. 28.√82 to 1 decimal place? (a) 9.1 (b) 8.9 (c) 9.0 (d) 8.8
  29. 29.√83 to 1 decimal place? (a) 9.1 (b) 8.9 (c) 9.0 (d) 8.8
  30. 30.Best estimate of 2637 ÷ 51? (a) 5300 (b) 530 (c) 53
  31. 31.√20 to 1 decimal place? (a) 4.5 (b) 4.4 (c) 4.6 (d) 4.7
  32. 32.√38 to 1 decimal place? (a) 6.3 (b) 6.2 (c) 6.1 (d) 6.4
  33. 33.√46 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 7.0 (d) 7.1
  34. 34.Best estimate of 4864 ÷ 73? (a) 6900 (b) 69 (c) 690
  35. 35.Best estimate of 2851 ÷ 69? (a) 41 (b) 410 (c) 4100
  36. 36.Best estimate of 3011 ÷ 56? (a) 5000 (b) 50 (c) 500
  37. 37.Best estimate of 2022 ÷ 22? (a) 10100 (b) 1010 (c) 101
  38. 38.Best estimate of 4177 ÷ 82? (a) 52 (b) 520 (c) 5200
  39. 39.Best estimate of 784 ÷ 58? (a) 130 (b) 1300 (c) 13
  40. 40.√35 to 1 decimal place? (a) 6.2 (b) 5.9 (c) 6.1 (d) 6.0

Answer key

  1. 6.1
  2. 21
  3. 8.9
  4. 9.6
  5. 7.8
  6. 67
  7. 22
  8. 8.1
  9. 27
  10. 8.6
  11. 72
  12. 72
  13. 42
  14. 22
  15. 8.1
  16. 5.7
  17. 57
  18. 5.4
  19. 55
  20. 8.5
  21. 20
  22. 53
  23. 13
  24. 60
  25. 6.7
  26. 68
  27. 17
  28. 9.1
  29. 9.1
  30. 53
  31. 4.5
  32. 6.2
  33. 6.8
  34. 69
  35. 41
  36. 50
  37. 101
  38. 52
  39. 13
  40. 5.9

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