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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 640 · 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.√83 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.1 (d) 9.0
  2. 2.Best estimate of 2890 ÷ 76? (a) 360 (b) 3600 (c) 36
  3. 3.Best estimate of 1762 ÷ 22? (a) 88 (b) 8800 (c) 880
  4. 4.Best estimate of 4140 ÷ 82? (a) 52 (b) 520 (c) 5200
  5. 5.√37 to 1 decimal place? (a) 6.2 (b) 5.9 (c) 6.0 (d) 6.1
  6. 6.√98 to 1 decimal place? (a) 10.1 (b) 10.2 (c) 10.0 (d) 9.9
  7. 7.Best estimate of 2111 ÷ 71? (a) 300 (b) 3000 (c) 30
  8. 8.√56 to 1 decimal place? (a) 7.7 (b) 7.4 (c) 7.6 (d) 7.5
  9. 9.√61 to 1 decimal place? (a) 7.7 (b) 7.9 (c) 7.8 (d) 8.0
  10. 10.√87 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.5 (d) 9.6
  11. 11.Best estimate of 1771 ÷ 82? (a) 220 (b) 2200 (c) 22
  12. 12.√50 to 1 decimal place? (a) 7.1 (b) 6.9 (c) 7.0 (d) 6.8
  13. 13.Best estimate of 2614 ÷ 73? (a) 370 (b) 3700 (c) 37
  14. 14.√96 to 1 decimal place? (a) 9.8 (b) 9.6 (c) 9.7 (d) 9.5
  15. 15.Best estimate of 3881 ÷ 72? (a) 55 (b) 5500 (c) 550
  16. 16.√41 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 6.3 (d) 6.4
  17. 17.Best estimate of 1111 ÷ 23? (a) 56 (b) 560 (c) 5600
  18. 18.√51 to 1 decimal place? (a) 7.4 (b) 7.1 (c) 7.3 (d) 7.2
  19. 19.Best estimate of 1521 ÷ 44? (a) 38 (b) 380 (c) 3800
  20. 20.√40 to 1 decimal place? (a) 6.5 (b) 6.3 (c) 6.6 (d) 6.4
  21. 21.√20 to 1 decimal place? (a) 4.5 (b) 4.4 (c) 4.3 (d) 4.6
  22. 22.√69 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.0 (d) 8.3
  23. 23.√23 to 1 decimal place? (a) 5.1 (b) 4.8 (c) 5.0 (d) 4.9
  24. 24.Best estimate of 6147 ÷ 87? (a) 680 (b) 68 (c) 6800
  25. 25.Best estimate of 4254 ÷ 51? (a) 85 (b) 8500 (c) 850
  26. 26.Best estimate of 864 ÷ 26? (a) 2900 (b) 290 (c) 29
  27. 27.Best estimate of 2067 ÷ 63? (a) 3400 (b) 34 (c) 340
  28. 28.Best estimate of 1204 ÷ 88? (a) 1300 (b) 130 (c) 13
  29. 29.Best estimate of 6971 ÷ 82? (a) 8700 (b) 870 (c) 87
  30. 30.√80 to 1 decimal place? (a) 9.0 (b) 8.7 (c) 8.9 (d) 8.8
  31. 31.Best estimate of 5619 ÷ 62? (a) 94 (b) 9400 (c) 940
  32. 32.√27 to 1 decimal place? (a) 5.2 (b) 5.4 (c) 5.3 (d) 5.1
  33. 33.√31 to 1 decimal place? (a) 5.6 (b) 5.5 (c) 5.4 (d) 5.7
  34. 34.Best estimate of 4367 ÷ 66? (a) 62 (b) 6200 (c) 620
  35. 35.Best estimate of 1824 ÷ 63? (a) 30 (b) 300 (c) 3000
  36. 36.Best estimate of 790 ÷ 39? (a) 2000 (b) 20 (c) 200
  37. 37.√67 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.5 (d) 8.4
  38. 38.√22 to 1 decimal place? (a) 4.7 (b) 4.8 (c) 4.6 (d) 4.9
  39. 39.√84 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.1 (d) 9.0
  40. 40.√85 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 9.4 (d) 9.3

Answer key

  1. 9.1
  2. 36
  3. 88
  4. 52
  5. 6.1
  6. 9.9
  7. 30
  8. 7.5
  9. 7.8
  10. 9.3
  11. 22
  12. 7.1
  13. 37
  14. 9.8
  15. 55
  16. 6.4
  17. 56
  18. 7.1
  19. 38
  20. 6.3
  21. 4.5
  22. 8.3
  23. 4.8
  24. 68
  25. 85
  26. 29
  27. 34
  28. 13
  29. 87
  30. 8.9
  31. 94
  32. 5.2
  33. 5.6
  34. 62
  35. 30
  36. 20
  37. 8.2
  38. 4.7
  39. 9.2
  40. 9.2

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