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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 783 · 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.Best estimate of 2702 ÷ 58? (a) 450 (b) 4500 (c) 45
  2. 2.√47 to 1 decimal place? (a) 6.7 (b) 6.9 (c) 6.8 (d) 6.6
  3. 3.Best estimate of 3613 ÷ 64? (a) 600 (b) 60 (c) 6000
  4. 4.Best estimate of 770 ÷ 56? (a) 1300 (b) 130 (c) 13
  5. 5.√41 to 1 decimal place? (a) 6.3 (b) 6.5 (c) 6.6 (d) 6.4
  6. 6.Best estimate of 617 ÷ 24? (a) 3100 (b) 31 (c) 310
  7. 7.Best estimate of 422 ÷ 22? (a) 2100 (b) 210 (c) 21
  8. 8.Best estimate of 4331 ÷ 59? (a) 72 (b) 720 (c) 7200
  9. 9.Best estimate of 3217 ÷ 68? (a) 46 (b) 460 (c) 4600
  10. 10.√82 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 9.1 (d) 9.2
  11. 11.√98 to 1 decimal place? (a) 10.1 (b) 10.0 (c) 9.9 (d) 9.8
  12. 12.Best estimate of 5978 ÷ 67? (a) 850 (b) 8500 (c) 85
  13. 13.√76 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.7 (d) 9.0
  14. 14.Best estimate of 3036 ÷ 73? (a) 4300 (b) 43 (c) 430
  15. 15.√55 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.4 (d) 7.3
  16. 16.√32 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.7 (d) 5.6
  17. 17.Best estimate of 1597 ÷ 29? (a) 53 (b) 530 (c) 5300
  18. 18.√87 to 1 decimal place? (a) 9.5 (b) 9.2 (c) 9.4 (d) 9.3
  19. 19.√45 to 1 decimal place? (a) 6.7 (b) 6.9 (c) 6.8 (d) 7.0
  20. 20.√74 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.7 (d) 8.8
  21. 21.Best estimate of 1533 ÷ 44? (a) 38 (b) 3800 (c) 380
  22. 22.Best estimate of 2992 ÷ 82? (a) 3700 (b) 370 (c) 37
  23. 23.√22 to 1 decimal place? (a) 4.7 (b) 4.9 (c) 4.6 (d) 4.8
  24. 24.√63 to 1 decimal place? (a) 7.9 (b) 7.7 (c) 8.0 (d) 7.8
  25. 25.Best estimate of 1711 ÷ 42? (a) 430 (b) 43 (c) 4300
  26. 26.√30 to 1 decimal place? (a) 5.6 (b) 5.4 (c) 5.5 (d) 5.3
  27. 27.√23 to 1 decimal place? (a) 5.1 (b) 4.8 (c) 4.9 (d) 5.0
  28. 28.√75 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.5 (d) 8.8
  29. 29.√86 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 9.4 (d) 9.3
  30. 30.√69 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.6 (d) 8.3
  31. 31.√78 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.8 (d) 8.7
  32. 32.Best estimate of 4855 ÷ 82? (a) 61 (b) 6100 (c) 610
  33. 33.Best estimate of 4432 ÷ 78? (a) 550 (b) 5500 (c) 55
  34. 34.Best estimate of 1231 ÷ 86? (a) 140 (b) 1400 (c) 14
  35. 35.Best estimate of 601 ÷ 38? (a) 150 (b) 15 (c) 1500
  36. 36.Best estimate of 1718 ÷ 56? (a) 290 (b) 2900 (c) 29
  37. 37.Best estimate of 952 ÷ 37? (a) 24 (b) 240 (c) 2400
  38. 38.√20 to 1 decimal place? (a) 4.7 (b) 4.6 (c) 4.5 (d) 4.8
  39. 39.Best estimate of 1497 ÷ 26? (a) 50 (b) 5000 (c) 500
  40. 40.Best estimate of 1630 ÷ 56? (a) 2700 (b) 270 (c) 27

Answer key

  1. 45
  2. 6.9
  3. 60
  4. 13
  5. 6.4
  6. 31
  7. 21
  8. 72
  9. 46
  10. 9.1
  11. 9.9
  12. 85
  13. 8.7
  14. 43
  15. 7.4
  16. 5.7
  17. 53
  18. 9.3
  19. 6.7
  20. 8.6
  21. 38
  22. 37
  23. 4.7
  24. 7.9
  25. 43
  26. 5.5
  27. 4.8
  28. 8.7
  29. 9.3
  30. 8.3
  31. 8.8
  32. 61
  33. 55
  34. 14
  35. 15
  36. 29
  37. 24
  38. 4.5
  39. 50
  40. 27

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