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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 743 · 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.√67 to 1 decimal place? (a) 8.5 (b) 8.3 (c) 8.2 (d) 8.4
  2. 2.√85 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 8.9 (d) 9.1
  3. 3.Best estimate of 4432 ÷ 88? (a) 4900 (b) 49 (c) 490
  4. 4.Best estimate of 3737 ÷ 81? (a) 4700 (b) 47 (c) 470
  5. 5.√94 to 1 decimal place? (a) 10.0 (b) 9.9 (c) 9.8 (d) 9.7
  6. 6.Best estimate of 2928 ÷ 41? (a) 7300 (b) 730 (c) 73
  7. 7.Best estimate of 4569 ÷ 64? (a) 760 (b) 76 (c) 7600
  8. 8.√28 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.0 (d) 5.1
  9. 9.√78 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.7 (d) 8.9
  10. 10.Best estimate of 1876 ÷ 31? (a) 63 (b) 630 (c) 6300
  11. 11.Best estimate of 1023 ÷ 23? (a) 5100 (b) 510 (c) 51
  12. 12.Best estimate of 3210 ÷ 43? (a) 800 (b) 8000 (c) 80
  13. 13.√23 to 1 decimal place? (a) 4.5 (b) 4.8 (c) 4.6 (d) 4.7
  14. 14.√65 to 1 decimal place? (a) 8.0 (b) 7.9 (c) 8.1 (d) 7.8
  15. 15.Best estimate of 7283 ÷ 82? (a) 910 (b) 91 (c) 9100
  16. 16.√55 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.7 (d) 7.6
  17. 17.Best estimate of 1152 ÷ 42? (a) 290 (b) 29 (c) 2900
  18. 18.Best estimate of 2909 ÷ 86? (a) 320 (b) 32 (c) 3200
  19. 19.Best estimate of 1199 ÷ 86? (a) 1300 (b) 130 (c) 13
  20. 20.Best estimate of 2259 ÷ 88? (a) 250 (b) 2500 (c) 25
  21. 21.Best estimate of 1711 ÷ 27? (a) 57 (b) 570 (c) 5700
  22. 22.√58 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 7.9 (d) 7.6
  23. 23.Best estimate of 4310 ÷ 81? (a) 5400 (b) 540 (c) 54
  24. 24.Best estimate of 7413 ÷ 86? (a) 82 (b) 820 (c) 8200
  25. 25.Best estimate of 1033 ÷ 86? (a) 1100 (b) 11 (c) 110
  26. 26.√89 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.5 (d) 9.6
  27. 27.Best estimate of 1222 ÷ 36? (a) 31 (b) 310 (c) 3100
  28. 28.Best estimate of 3234 ÷ 74? (a) 46 (b) 4600 (c) 460
  29. 29.Best estimate of 1717 ÷ 74? (a) 2500 (b) 25 (c) 250
  30. 30.√63 to 1 decimal place? (a) 8.0 (b) 8.2 (c) 8.1 (d) 7.9
  31. 31.Best estimate of 2624 ÷ 81? (a) 330 (b) 3300 (c) 33
  32. 32.Best estimate of 1786 ÷ 28? (a) 60 (b) 6000 (c) 600
  33. 33.Best estimate of 2193 ÷ 33? (a) 730 (b) 73 (c) 7300
  34. 34.Best estimate of 3377 ÷ 86? (a) 3800 (b) 38 (c) 380
  35. 35.√74 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.9 (d) 8.6
  36. 36.√61 to 1 decimal place? (a) 7.6 (b) 7.7 (c) 7.8 (d) 7.5
  37. 37.√56 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.7 (d) 7.8
  38. 38.Best estimate of 1040 ÷ 59? (a) 17 (b) 170 (c) 1700
  39. 39.√53 to 1 decimal place? (a) 7.3 (b) 7.1 (c) 7.2 (d) 7.0
  40. 40.√51 to 1 decimal place? (a) 7.3 (b) 7.0 (c) 7.2 (d) 7.1

Answer key

  1. 8.2
  2. 9.2
  3. 49
  4. 47
  5. 9.7
  6. 73
  7. 76
  8. 5.3
  9. 8.8
  10. 63
  11. 51
  12. 80
  13. 4.8
  14. 8.1
  15. 91
  16. 7.4
  17. 29
  18. 32
  19. 13
  20. 25
  21. 57
  22. 7.6
  23. 54
  24. 82
  25. 11
  26. 9.4
  27. 31
  28. 46
  29. 25
  30. 7.9
  31. 33
  32. 60
  33. 73
  34. 38
  35. 8.6
  36. 7.8
  37. 7.5
  38. 17
  39. 7.3
  40. 7.1

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