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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 772 · 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 1867 ÷ 74? (a) 2700 (b) 270 (c) 27
  2. 2.Best estimate of 4526 ÷ 71? (a) 65 (b) 6500 (c) 650
  3. 3.√40 to 1 decimal place? (a) 6.4 (b) 6.2 (c) 6.3 (d) 6.1
  4. 4.Best estimate of 3650 ÷ 66? (a) 520 (b) 52 (c) 5200
  5. 5.√82 to 1 decimal place? (a) 8.8 (b) 9.1 (c) 9.0 (d) 8.9
  6. 6.Best estimate of 2534 ÷ 69? (a) 36 (b) 3600 (c) 360
  7. 7.Best estimate of 3586 ÷ 66? (a) 51 (b) 5100 (c) 510
  8. 8.Best estimate of 4280 ÷ 72? (a) 610 (b) 61 (c) 6100
  9. 9.√50 to 1 decimal place? (a) 7.0 (b) 7.3 (c) 7.2 (d) 7.1
  10. 10.√61 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 8.0 (d) 8.1
  11. 11.√46 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.9 (d) 7.0
  12. 12.Best estimate of 2180 ÷ 36? (a) 5500 (b) 550 (c) 55
  13. 13.Best estimate of 2787 ÷ 86? (a) 3100 (b) 31 (c) 310
  14. 14.Best estimate of 2023 ÷ 24? (a) 10100 (b) 1010 (c) 101
  15. 15.√78 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.7 (d) 8.9
  16. 16.√74 to 1 decimal place? (a) 8.7 (b) 8.4 (c) 8.6 (d) 8.5
  17. 17.√66 to 1 decimal place? (a) 8.2 (b) 8.4 (c) 8.1 (d) 8.3
  18. 18.Best estimate of 2839 ÷ 66? (a) 410 (b) 4100 (c) 41
  19. 19.√84 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 8.9 (d) 9.2
  20. 20.Best estimate of 2995 ÷ 62? (a) 50 (b) 5000 (c) 500
  21. 21.√92 to 1 decimal place? (a) 9.5 (b) 9.8 (c) 9.6 (d) 9.7
  22. 22.Best estimate of 3039 ÷ 54? (a) 610 (b) 6100 (c) 61
  23. 23.Best estimate of 2726 ÷ 73? (a) 39 (b) 390 (c) 3900
  24. 24.√96 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 9.9 (d) 9.6
  25. 25.Best estimate of 5347 ÷ 78? (a) 6700 (b) 670 (c) 67
  26. 26.√24 to 1 decimal place? (a) 5.0 (b) 4.8 (c) 4.9 (d) 5.1
  27. 27.√65 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 8.3 (d) 8.2
  28. 28.√79 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 8.8 (d) 8.7
  29. 29.Best estimate of 1170 ÷ 23? (a) 590 (b) 59 (c) 5900
  30. 30.Best estimate of 6151 ÷ 81? (a) 7700 (b) 770 (c) 77
  31. 31.√20 to 1 decimal place? (a) 4.4 (b) 4.3 (c) 4.6 (d) 4.5
  32. 32.Best estimate of 1545 ÷ 82? (a) 1900 (b) 190 (c) 19
  33. 33.Best estimate of 1077 ÷ 23? (a) 5400 (b) 540 (c) 54
  34. 34.Best estimate of 7048 ÷ 76? (a) 880 (b) 8800 (c) 88
  35. 35.Best estimate of 5632 ÷ 72? (a) 800 (b) 80 (c) 8000
  36. 36.Best estimate of 2686 ÷ 73? (a) 3800 (b) 380 (c) 38
  37. 37.Best estimate of 3507 ÷ 47? (a) 700 (b) 7000 (c) 70
  38. 38.Best estimate of 1076 ÷ 52? (a) 220 (b) 22 (c) 2200
  39. 39.√72 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.5 (d) 8.4
  40. 40.√83 to 1 decimal place? (a) 9.3 (b) 9.1 (c) 9.4 (d) 9.2

Answer key

  1. 27
  2. 65
  3. 6.3
  4. 52
  5. 9.1
  6. 36
  7. 51
  8. 61
  9. 7.1
  10. 7.8
  11. 6.8
  12. 55
  13. 31
  14. 101
  15. 8.8
  16. 8.6
  17. 8.1
  18. 41
  19. 9.2
  20. 50
  21. 9.6
  22. 61
  23. 39
  24. 9.8
  25. 67
  26. 4.9
  27. 8.1
  28. 8.9
  29. 59
  30. 77
  31. 4.5
  32. 19
  33. 54
  34. 88
  35. 80
  36. 38
  37. 70
  38. 22
  39. 8.5
  40. 9.1

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