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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 848 · 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.√92 to 1 decimal place? (a) 9.6 (b) 9.4 (c) 9.5 (d) 9.7
  2. 2.Best estimate of 3561 ÷ 62? (a) 59 (b) 5900 (c) 590
  3. 3.Best estimate of 620 ÷ 36? (a) 160 (b) 1600 (c) 16
  4. 4.Best estimate of 683 ÷ 23? (a) 3400 (b) 34 (c) 340
  5. 5.Best estimate of 1190 ÷ 21? (a) 6000 (b) 60 (c) 600
  6. 6.Best estimate of 5488 ÷ 69? (a) 78 (b) 7800 (c) 780
  7. 7.√61 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 7.6 (d) 7.5
  8. 8.√77 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.9 (d) 8.8
  9. 9.√74 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.4 (d) 8.7
  10. 10.√53 to 1 decimal place? (a) 7.5 (b) 7.3 (c) 7.4 (d) 7.6
  11. 11.Best estimate of 1594 ÷ 22? (a) 80 (b) 8000 (c) 800
  12. 12.√29 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.6 (d) 5.7
  13. 13.√63 to 1 decimal place? (a) 7.7 (b) 7.9 (c) 7.8 (d) 7.6
  14. 14.Best estimate of 1422 ÷ 31? (a) 4700 (b) 470 (c) 47
  15. 15.√35 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.9 (d) 5.6
  16. 16.√26 to 1 decimal place? (a) 5.2 (b) 5.1 (c) 5.3 (d) 5.0
  17. 17.Best estimate of 1954 ÷ 23? (a) 98 (b) 980 (c) 9800
  18. 18.Best estimate of 2034 ÷ 44? (a) 5100 (b) 51 (c) 510
  19. 19.√37 to 1 decimal place? (a) 6.1 (b) 6.0 (c) 6.2 (d) 6.3
  20. 20.√62 to 1 decimal place? (a) 7.6 (b) 7.7 (c) 7.9 (d) 7.8
  21. 21.Best estimate of 1631 ÷ 32? (a) 5400 (b) 54 (c) 540
  22. 22.√40 to 1 decimal place? (a) 6.6 (b) 6.4 (c) 6.5 (d) 6.3
  23. 23.√55 to 1 decimal place? (a) 7.5 (b) 7.7 (c) 7.6 (d) 7.4
  24. 24.Best estimate of 2292 ÷ 42? (a) 57 (b) 570 (c) 5700
  25. 25.Best estimate of 2213 ÷ 33? (a) 740 (b) 74 (c) 7400
  26. 26.√43 to 1 decimal place? (a) 6.4 (b) 6.6 (c) 6.5 (d) 6.3
  27. 27.Best estimate of 1518 ÷ 37? (a) 380 (b) 3800 (c) 38
  28. 28.√84 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.1 (d) 9.0
  29. 29.√42 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.6 (d) 6.3
  30. 30.Best estimate of 3159 ÷ 82? (a) 39 (b) 390 (c) 3900
  31. 31.Best estimate of 1168 ÷ 32? (a) 3900 (b) 390 (c) 39
  32. 32.√28 to 1 decimal place? (a) 5.3 (b) 5.6 (c) 5.4 (d) 5.5
  33. 33.√86 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.3 (d) 9.6
  34. 34.Best estimate of 1270 ÷ 26? (a) 420 (b) 4200 (c) 42
  35. 35.√96 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 10.1 (d) 10.0
  36. 36.Best estimate of 2641 ÷ 63? (a) 440 (b) 4400 (c) 44
  37. 37.√83 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 8.9 (d) 9.1
  38. 38.√38 to 1 decimal place? (a) 6.0 (b) 6.1 (c) 6.3 (d) 6.2
  39. 39.Best estimate of 3238 ÷ 49? (a) 650 (b) 65 (c) 6500
  40. 40.Best estimate of 3762 ÷ 56? (a) 63 (b) 6300 (c) 630

Answer key

  1. 9.6
  2. 59
  3. 16
  4. 34
  5. 60
  6. 78
  7. 7.8
  8. 8.8
  9. 8.6
  10. 7.3
  11. 80
  12. 5.4
  13. 7.9
  14. 47
  15. 5.9
  16. 5.1
  17. 98
  18. 51
  19. 6.1
  20. 7.9
  21. 54
  22. 6.3
  23. 7.4
  24. 57
  25. 74
  26. 6.6
  27. 38
  28. 9.2
  29. 6.5
  30. 39
  31. 39
  32. 5.3
  33. 9.3
  34. 42
  35. 9.8
  36. 44
  37. 9.1
  38. 6.2
  39. 65
  40. 63

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