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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 796 · 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.√63 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.9 (d) 7.8
  2. 2.Best estimate of 2314 ÷ 36? (a) 5800 (b) 58 (c) 580
  3. 3.√76 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 8.7 (d) 8.8
  4. 4.√26 to 1 decimal place? (a) 4.9 (b) 5.2 (c) 5.1 (d) 5.0
  5. 5.Best estimate of 1133 ÷ 34? (a) 38 (b) 3800 (c) 380
  6. 6.√61 to 1 decimal place? (a) 7.9 (b) 7.7 (c) 7.8 (d) 7.6
  7. 7.Best estimate of 2560 ÷ 42? (a) 640 (b) 64 (c) 6400
  8. 8.Best estimate of 7637 ÷ 83? (a) 950 (b) 9500 (c) 95
  9. 9.Best estimate of 5558 ÷ 61? (a) 930 (b) 93 (c) 9300
  10. 10.Best estimate of 1176 ÷ 33? (a) 39 (b) 3900 (c) 390
  11. 11.Best estimate of 2638 ÷ 72? (a) 38 (b) 380 (c) 3800
  12. 12.√21 to 1 decimal place? (a) 4.3 (b) 4.6 (c) 4.5 (d) 4.4
  13. 13.Best estimate of 3198 ÷ 34? (a) 10700 (b) 107 (c) 1070
  14. 14.√65 to 1 decimal place? (a) 8.3 (b) 8.1 (c) 8.0 (d) 8.2
  15. 15.√38 to 1 decimal place? (a) 6.3 (b) 6.5 (c) 6.2 (d) 6.4
  16. 16.√40 to 1 decimal place? (a) 6.4 (b) 6.1 (c) 6.3 (d) 6.2
  17. 17.√47 to 1 decimal place? (a) 7.0 (b) 6.8 (c) 6.9 (d) 7.1
  18. 18.√98 to 1 decimal place? (a) 10.0 (b) 9.7 (c) 9.9 (d) 9.8
  19. 19.Best estimate of 2077 ÷ 53? (a) 420 (b) 42 (c) 4200
  20. 20.Best estimate of 459 ÷ 26? (a) 1500 (b) 15 (c) 150
  21. 21.√85 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.3 (d) 9.2
  22. 22.Best estimate of 1073 ÷ 38? (a) 270 (b) 27 (c) 2700
  23. 23.√43 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.5 (d) 6.4
  24. 24.√41 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.4 (d) 6.5
  25. 25.Best estimate of 2806 ÷ 72? (a) 4000 (b) 400 (c) 40
  26. 26.Best estimate of 1440 ÷ 21? (a) 72 (b) 720 (c) 7200
  27. 27.Best estimate of 3720 ÷ 74? (a) 53 (b) 5300 (c) 530
  28. 28.Best estimate of 2849 ÷ 37? (a) 7100 (b) 710 (c) 71
  29. 29.Best estimate of 973 ÷ 36? (a) 24 (b) 2400 (c) 240
  30. 30.√48 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.8 (d) 6.9
  31. 31.√82 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 9.2 (d) 9.3
  32. 32.Best estimate of 1477 ÷ 49? (a) 300 (b) 3000 (c) 30
  33. 33.√56 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.3 (d) 7.6
  34. 34.Best estimate of 2263 ÷ 32? (a) 7500 (b) 75 (c) 750
  35. 35.Best estimate of 1350 ÷ 32? (a) 450 (b) 4500 (c) 45
  36. 36.Best estimate of 1148 ÷ 24? (a) 5700 (b) 57 (c) 570
  37. 37.√94 to 1 decimal place? (a) 9.7 (b) 9.9 (c) 9.8 (d) 9.6
  38. 38.√55 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.6 (d) 7.3
  39. 39.√31 to 1 decimal place? (a) 5.6 (b) 5.9 (c) 5.8 (d) 5.7
  40. 40.Best estimate of 1625 ÷ 84? (a) 2000 (b) 20 (c) 200

Answer key

  1. 7.9
  2. 58
  3. 8.7
  4. 5.1
  5. 38
  6. 7.8
  7. 64
  8. 95
  9. 93
  10. 39
  11. 38
  12. 4.6
  13. 107
  14. 8.1
  15. 6.2
  16. 6.3
  17. 6.9
  18. 9.9
  19. 42
  20. 15
  21. 9.2
  22. 27
  23. 6.6
  24. 6.4
  25. 40
  26. 72
  27. 53
  28. 71
  29. 24
  30. 6.9
  31. 9.1
  32. 30
  33. 7.5
  34. 75
  35. 45
  36. 57
  37. 9.7
  38. 7.4
  39. 5.6
  40. 20

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