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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 704 · 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.√84 to 1 decimal place? (a) 9.2 (b) 9.5 (c) 9.3 (d) 9.4
  2. 2.√76 to 1 decimal place? (a) 9.0 (b) 8.7 (c) 8.9 (d) 8.8
  3. 3.Best estimate of 3531 ÷ 61? (a) 590 (b) 5900 (c) 59
  4. 4.Best estimate of 1899 ÷ 24? (a) 950 (b) 95 (c) 9500
  5. 5.√75 to 1 decimal place? (a) 8.7 (b) 8.4 (c) 8.5 (d) 8.6
  6. 6.Best estimate of 2577 ÷ 78? (a) 3200 (b) 32 (c) 320
  7. 7.√28 to 1 decimal place? (a) 5.1 (b) 5.3 (c) 5.2 (d) 5.0
  8. 8.Best estimate of 2107 ÷ 52? (a) 42 (b) 4200 (c) 420
  9. 9.Best estimate of 3321 ÷ 39? (a) 8300 (b) 83 (c) 830
  10. 10.Best estimate of 1588 ÷ 56? (a) 260 (b) 26 (c) 2600
  11. 11.√31 to 1 decimal place? (a) 5.5 (b) 5.7 (c) 5.4 (d) 5.6
  12. 12.√74 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.9 (d) 8.7
  13. 13.Best estimate of 2365 ÷ 57? (a) 3900 (b) 390 (c) 39
  14. 14.Best estimate of 2749 ÷ 44? (a) 6900 (b) 69 (c) 690
  15. 15.Best estimate of 5170 ÷ 58? (a) 86 (b) 860 (c) 8600
  16. 16.√65 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 8.2 (d) 7.9
  17. 17.√90 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.5 (d) 9.4
  18. 18.Best estimate of 2614 ÷ 37? (a) 6500 (b) 650 (c) 65
  19. 19.√77 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 8.8 (d) 8.9
  20. 20.Best estimate of 2635 ÷ 36? (a) 6600 (b) 66 (c) 660
  21. 21.Best estimate of 1698 ÷ 89? (a) 19 (b) 190 (c) 1900
  22. 22.√78 to 1 decimal place? (a) 9.1 (b) 8.9 (c) 9.0 (d) 8.8
  23. 23.√56 to 1 decimal place? (a) 7.5 (b) 7.7 (c) 7.6 (d) 7.4
  24. 24.√58 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.8 (d) 7.5
  25. 25.Best estimate of 1455 ÷ 21? (a) 73 (b) 730 (c) 7300
  26. 26.Best estimate of 1995 ÷ 31? (a) 6700 (b) 670 (c) 67
  27. 27.Best estimate of 6787 ÷ 72? (a) 970 (b) 97 (c) 9700
  28. 28.Best estimate of 2657 ÷ 73? (a) 380 (b) 3800 (c) 38
  29. 29.√26 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.2 (d) 5.1
  30. 30.Best estimate of 2020 ÷ 67? (a) 290 (b) 2900 (c) 29
  31. 31.Best estimate of 2773 ÷ 86? (a) 3100 (b) 310 (c) 31
  32. 32.√44 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.5 (d) 6.8
  33. 33.Best estimate of 5116 ÷ 58? (a) 850 (b) 85 (c) 8500
  34. 34.√55 to 1 decimal place? (a) 7.5 (b) 7.3 (c) 7.6 (d) 7.4
  35. 35.Best estimate of 1210 ÷ 72? (a) 1700 (b) 170 (c) 17
  36. 36.Best estimate of 748 ÷ 27? (a) 250 (b) 2500 (c) 25
  37. 37.Best estimate of 2082 ÷ 43? (a) 5200 (b) 520 (c) 52
  38. 38.√24 to 1 decimal place? (a) 4.7 (b) 4.8 (c) 4.6 (d) 4.9
  39. 39.Best estimate of 3904 ÷ 88? (a) 43 (b) 4300 (c) 430
  40. 40.Best estimate of 3270 ÷ 36? (a) 820 (b) 8200 (c) 82

Answer key

  1. 9.2
  2. 8.7
  3. 59
  4. 95
  5. 8.7
  6. 32
  7. 5.3
  8. 42
  9. 83
  10. 26
  11. 5.6
  12. 8.6
  13. 39
  14. 69
  15. 86
  16. 8.1
  17. 9.5
  18. 65
  19. 8.8
  20. 66
  21. 19
  22. 8.8
  23. 7.5
  24. 7.6
  25. 73
  26. 67
  27. 97
  28. 38
  29. 5.1
  30. 29
  31. 31
  32. 6.6
  33. 85
  34. 7.4
  35. 17
  36. 25
  37. 52
  38. 4.9
  39. 43
  40. 82

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