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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 817 · 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 4957 ÷ 56? (a) 8300 (b) 830 (c) 83
  2. 2.√26 to 1 decimal place? (a) 4.9 (b) 5.0 (c) 5.2 (d) 5.1
  3. 3.√78 to 1 decimal place? (a) 8.9 (b) 9.1 (c) 9.0 (d) 8.8
  4. 4.√38 to 1 decimal place? (a) 6.5 (b) 6.2 (c) 6.3 (d) 6.4
  5. 5.Best estimate of 1261 ÷ 21? (a) 6300 (b) 630 (c) 63
  6. 6.Best estimate of 1966 ÷ 32? (a) 6600 (b) 660 (c) 66
  7. 7.Best estimate of 1494 ÷ 89? (a) 1700 (b) 17 (c) 170
  8. 8.Best estimate of 3570 ÷ 66? (a) 51 (b) 510 (c) 5100
  9. 9.√84 to 1 decimal place? (a) 9.3 (b) 9.1 (c) 9.4 (d) 9.2
  10. 10.√32 to 1 decimal place? (a) 5.7 (b) 5.9 (c) 6.0 (d) 5.8
  11. 11.Best estimate of 3751 ÷ 57? (a) 6300 (b) 630 (c) 63
  12. 12.Best estimate of 450 ÷ 33? (a) 15 (b) 150 (c) 1500
  13. 13.√27 to 1 decimal place? (a) 5.4 (b) 5.5 (c) 5.3 (d) 5.2
  14. 14.Best estimate of 2289 ÷ 24? (a) 11400 (b) 114 (c) 1140
  15. 15.√58 to 1 decimal place? (a) 7.8 (b) 7.5 (c) 7.7 (d) 7.6
  16. 16.Best estimate of 6087 ÷ 81? (a) 76 (b) 7600 (c) 760
  17. 17.√40 to 1 decimal place? (a) 6.0 (b) 6.1 (c) 6.2 (d) 6.3
  18. 18.Best estimate of 3212 ÷ 42? (a) 800 (b) 8000 (c) 80
  19. 19.Best estimate of 5799 ÷ 82? (a) 720 (b) 72 (c) 7200
  20. 20.Best estimate of 4904 ÷ 58? (a) 82 (b) 8200 (c) 820
  21. 21.√30 to 1 decimal place? (a) 5.5 (b) 5.6 (c) 5.8 (d) 5.7
  22. 22.Best estimate of 711 ÷ 39? (a) 18 (b) 1800 (c) 180
  23. 23.Best estimate of 3588 ÷ 46? (a) 720 (b) 72 (c) 7200
  24. 24.√41 to 1 decimal place? (a) 6.1 (b) 6.3 (c) 6.4 (d) 6.2
  25. 25.√65 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 8.2 (d) 7.9
  26. 26.Best estimate of 3445 ÷ 86? (a) 380 (b) 38 (c) 3800
  27. 27.Best estimate of 2062 ÷ 51? (a) 41 (b) 410 (c) 4100
  28. 28.Best estimate of 5268 ÷ 72? (a) 75 (b) 7500 (c) 750
  29. 29.√77 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.7 (d) 8.6
  30. 30.√72 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.3 (d) 8.6
  31. 31.√48 to 1 decimal place? (a) 7.1 (b) 6.9 (c) 7.2 (d) 7.0
  32. 32.Best estimate of 6036 ÷ 83? (a) 750 (b) 75 (c) 7500
  33. 33.√56 to 1 decimal place? (a) 7.3 (b) 7.5 (c) 7.4 (d) 7.2
  34. 34.Best estimate of 2061 ÷ 51? (a) 410 (b) 4100 (c) 41
  35. 35.√20 to 1 decimal place? (a) 4.4 (b) 4.5 (c) 4.6 (d) 4.7
  36. 36.Best estimate of 1381 ÷ 34? (a) 4600 (b) 460 (c) 46
  37. 37.Best estimate of 1038 ÷ 46? (a) 210 (b) 21 (c) 2100
  38. 38.Best estimate of 2470 ÷ 86? (a) 2700 (b) 270 (c) 27
  39. 39.Best estimate of 3004 ÷ 71? (a) 43 (b) 430 (c) 4300
  40. 40.Best estimate of 5325 ÷ 57? (a) 8900 (b) 89 (c) 890

Answer key

  1. 83
  2. 5.1
  3. 8.8
  4. 6.2
  5. 63
  6. 66
  7. 17
  8. 51
  9. 9.2
  10. 5.7
  11. 63
  12. 15
  13. 5.2
  14. 114
  15. 7.6
  16. 76
  17. 6.3
  18. 80
  19. 72
  20. 82
  21. 5.5
  22. 18
  23. 72
  24. 6.4
  25. 8.1
  26. 38
  27. 41
  28. 75
  29. 8.8
  30. 8.5
  31. 6.9
  32. 75
  33. 7.5
  34. 41
  35. 4.5
  36. 46
  37. 21
  38. 27
  39. 43
  40. 89

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