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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 40 · 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 4386 ÷ 51? (a) 880 (b) 88 (c) 8800
  2. 2.Best estimate of 2056 ÷ 41? (a) 510 (b) 5100 (c) 51
  3. 3.Best estimate of 3079 ÷ 46? (a) 62 (b) 620 (c) 6200
  4. 4.Best estimate of 6072 ÷ 71? (a) 8700 (b) 87 (c) 870
  5. 5.√96 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 9.7 (d) 9.6
  6. 6.√55 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.5 (d) 7.2
  7. 7.√78 to 1 decimal place? (a) 8.9 (b) 9.1 (c) 9.0 (d) 8.8
  8. 8.Best estimate of 3857 ÷ 54? (a) 77 (b) 770 (c) 7700
  9. 9.√85 to 1 decimal place? (a) 9.3 (b) 9.0 (c) 9.2 (d) 9.1
  10. 10.√26 to 1 decimal place? (a) 5.1 (b) 5.2 (c) 4.9 (d) 5.0
  11. 11.√31 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 5.7 (d) 5.6
  12. 12.Best estimate of 969 ÷ 42? (a) 24 (b) 2400 (c) 240
  13. 13.Best estimate of 1051 ÷ 32? (a) 350 (b) 3500 (c) 35
  14. 14.√43 to 1 decimal place? (a) 6.8 (b) 6.7 (c) 6.6 (d) 6.5
  15. 15.Best estimate of 1253 ÷ 32? (a) 420 (b) 42 (c) 4200
  16. 16.√35 to 1 decimal place? (a) 6.1 (b) 6.2 (c) 5.9 (d) 6.0
  17. 17.√23 to 1 decimal place? (a) 4.8 (b) 4.6 (c) 4.9 (d) 4.7
  18. 18.√59 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.4 (d) 7.7
  19. 19.√50 to 1 decimal place? (a) 7.3 (b) 7.1 (c) 7.0 (d) 7.2
  20. 20.√58 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.7 (d) 7.4
  21. 21.Best estimate of 4455 ÷ 87? (a) 500 (b) 50 (c) 5000
  22. 22.Best estimate of 3148 ÷ 46? (a) 630 (b) 63 (c) 6300
  23. 23.√32 to 1 decimal place? (a) 6.0 (b) 5.9 (c) 5.7 (d) 5.8
  24. 24.√48 to 1 decimal place? (a) 7.0 (b) 7.2 (c) 7.1 (d) 6.9
  25. 25.Best estimate of 5691 ÷ 66? (a) 810 (b) 8100 (c) 81
  26. 26.√84 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.3 (d) 9.0
  27. 27.√40 to 1 decimal place? (a) 6.5 (b) 6.3 (c) 6.4 (d) 6.2
  28. 28.√62 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 7.9 (d) 8.2
  29. 29.Best estimate of 1002 ÷ 23? (a) 500 (b) 5000 (c) 50
  30. 30.Best estimate of 6077 ÷ 77? (a) 760 (b) 76 (c) 7600
  31. 31.√38 to 1 decimal place? (a) 6.1 (b) 6.3 (c) 6.4 (d) 6.2
  32. 32.√34 to 1 decimal place? (a) 5.8 (b) 6.1 (c) 5.9 (d) 6.0
  33. 33.√98 to 1 decimal place? (a) 10.1 (b) 10.2 (c) 10.0 (d) 9.9
  34. 34.√63 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 8.0 (d) 7.9
  35. 35.Best estimate of 1740 ÷ 21? (a) 870 (b) 8700 (c) 87
  36. 36.Best estimate of 4774 ÷ 53? (a) 950 (b) 95 (c) 9500
  37. 37.Best estimate of 1872 ÷ 48? (a) 370 (b) 3700 (c) 37
  38. 38.Best estimate of 1489 ÷ 32? (a) 500 (b) 5000 (c) 50
  39. 39.Best estimate of 3571 ÷ 66? (a) 5100 (b) 51 (c) 510
  40. 40.√29 to 1 decimal place? (a) 5.6 (b) 5.5 (c) 5.4 (d) 5.3

Answer key

  1. 88
  2. 51
  3. 62
  4. 87
  5. 9.8
  6. 7.4
  7. 8.8
  8. 77
  9. 9.2
  10. 5.1
  11. 5.6
  12. 24
  13. 35
  14. 6.6
  15. 42
  16. 5.9
  17. 4.8
  18. 7.7
  19. 7.1
  20. 7.6
  21. 50
  22. 63
  23. 5.7
  24. 6.9
  25. 81
  26. 9.2
  27. 6.3
  28. 7.9
  29. 50
  30. 76
  31. 6.2
  32. 5.8
  33. 9.9
  34. 7.9
  35. 87
  36. 95
  37. 37
  38. 50
  39. 51
  40. 5.4

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