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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 917 · 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.√94 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 9.8 (d) 10.0
  2. 2.√21 to 1 decimal place? (a) 4.7 (b) 4.4 (c) 4.6 (d) 4.5
  3. 3.Best estimate of 1566 ÷ 22? (a) 7800 (b) 780 (c) 78
  4. 4.Best estimate of 4713 ÷ 58? (a) 7900 (b) 790 (c) 79
  5. 5.Best estimate of 3012 ÷ 59? (a) 50 (b) 5000 (c) 500
  6. 6.√48 to 1 decimal place? (a) 6.7 (b) 6.9 (c) 6.8 (d) 6.6
  7. 7.Best estimate of 2989 ÷ 73? (a) 4300 (b) 430 (c) 43
  8. 8.√78 to 1 decimal place? (a) 8.8 (b) 8.5 (c) 8.6 (d) 8.7
  9. 9.Best estimate of 3002 ÷ 66? (a) 43 (b) 4300 (c) 430
  10. 10.√28 to 1 decimal place? (a) 5.5 (b) 5.6 (c) 5.4 (d) 5.3
  11. 11.Best estimate of 4258 ÷ 59? (a) 7100 (b) 710 (c) 71
  12. 12.Best estimate of 3282 ÷ 66? (a) 47 (b) 470 (c) 4700
  13. 13.√55 to 1 decimal place? (a) 7.4 (b) 7.1 (c) 7.3 (d) 7.2
  14. 14.Best estimate of 2407 ÷ 26? (a) 8000 (b) 800 (c) 80
  15. 15.√86 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.2 (d) 9.1
  16. 16.√27 to 1 decimal place? (a) 5.2 (b) 5.1 (c) 5.0 (d) 4.9
  17. 17.Best estimate of 2655 ÷ 68? (a) 38 (b) 380 (c) 3800
  18. 18.√50 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 7.4 (d) 7.3
  19. 19.Best estimate of 2328 ÷ 52? (a) 4700 (b) 47 (c) 470
  20. 20.Best estimate of 1078 ÷ 53? (a) 220 (b) 2200 (c) 22
  21. 21.Best estimate of 2375 ÷ 71? (a) 3400 (b) 340 (c) 34
  22. 22.Best estimate of 4265 ÷ 73? (a) 61 (b) 610 (c) 6100
  23. 23.Best estimate of 4149 ÷ 44? (a) 1040 (b) 104 (c) 10400
  24. 24.√43 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.8 (d) 6.9
  25. 25.Best estimate of 440 ÷ 21? (a) 220 (b) 2200 (c) 22
  26. 26.√65 to 1 decimal place? (a) 7.9 (b) 8.1 (c) 8.0 (d) 7.8
  27. 27.√44 to 1 decimal place? (a) 6.7 (b) 6.5 (c) 6.6 (d) 6.4
  28. 28.Best estimate of 659 ÷ 29? (a) 2200 (b) 220 (c) 22
  29. 29.√37 to 1 decimal place? (a) 6.0 (b) 6.3 (c) 6.1 (d) 6.2
  30. 30.Best estimate of 7161 ÷ 89? (a) 8000 (b) 80 (c) 800
  31. 31.√96 to 1 decimal place? (a) 9.8 (b) 9.6 (c) 9.7 (d) 9.5
  32. 32.Best estimate of 793 ÷ 46? (a) 16 (b) 160 (c) 1600
  33. 33.√46 to 1 decimal place? (a) 6.6 (b) 6.9 (c) 6.8 (d) 6.7
  34. 34.Best estimate of 2166 ÷ 44? (a) 540 (b) 54 (c) 5400
  35. 35.Best estimate of 709 ÷ 36? (a) 180 (b) 18 (c) 1800
  36. 36.Best estimate of 1320 ÷ 41? (a) 33 (b) 330 (c) 3300
  37. 37.Best estimate of 1894 ÷ 59? (a) 320 (b) 32 (c) 3200
  38. 38.√85 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.5 (d) 9.3
  39. 39.Best estimate of 5819 ÷ 71? (a) 83 (b) 8300 (c) 830
  40. 40.Best estimate of 2500 ÷ 61? (a) 42 (b) 4200 (c) 420

Answer key

  1. 9.7
  2. 4.6
  3. 78
  4. 79
  5. 50
  6. 6.9
  7. 43
  8. 8.8
  9. 43
  10. 5.3
  11. 71
  12. 47
  13. 7.4
  14. 80
  15. 9.3
  16. 5.2
  17. 38
  18. 7.1
  19. 47
  20. 22
  21. 34
  22. 61
  23. 104
  24. 6.6
  25. 22
  26. 8.1
  27. 6.6
  28. 22
  29. 6.1
  30. 80
  31. 9.8
  32. 16
  33. 6.8
  34. 54
  35. 18
  36. 33
  37. 32
  38. 9.2
  39. 83
  40. 42

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