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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 160 · 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.√55 to 1 decimal place? (a) 7.7 (b) 7.5 (c) 7.4 (d) 7.6
  2. 2.Best estimate of 805 ÷ 57? (a) 130 (b) 1300 (c) 13
  3. 3.√37 to 1 decimal place? (a) 6.4 (b) 6.1 (c) 6.2 (d) 6.3
  4. 4.√65 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 7.9 (d) 7.8
  5. 5.Best estimate of 1121 ÷ 27? (a) 37 (b) 370 (c) 3700
  6. 6.√77 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 8.8 (d) 8.9
  7. 7.√92 to 1 decimal place? (a) 9.6 (b) 9.4 (c) 9.7 (d) 9.5
  8. 8.√27 to 1 decimal place? (a) 5.4 (b) 5.2 (c) 5.3 (d) 5.5
  9. 9.Best estimate of 2273 ÷ 87? (a) 250 (b) 2500 (c) 25
  10. 10.Best estimate of 2995 ÷ 39? (a) 750 (b) 7500 (c) 75
  11. 11.Best estimate of 1378 ÷ 44? (a) 34 (b) 3400 (c) 340
  12. 12.Best estimate of 2629 ÷ 28? (a) 880 (b) 88 (c) 8800
  13. 13.√76 to 1 decimal place? (a) 8.8 (b) 9.0 (c) 8.9 (d) 8.7
  14. 14.√42 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.7 (d) 6.4
  15. 15.Best estimate of 2248 ÷ 26? (a) 750 (b) 75 (c) 7500
  16. 16.Best estimate of 6386 ÷ 67? (a) 9100 (b) 910 (c) 91
  17. 17.√78 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.7 (d) 8.9
  18. 18.√32 to 1 decimal place? (a) 5.6 (b) 5.8 (c) 5.5 (d) 5.7
  19. 19.Best estimate of 2849 ÷ 41? (a) 710 (b) 71 (c) 7100
  20. 20.Best estimate of 2799 ÷ 76? (a) 35 (b) 350 (c) 3500
  21. 21.√89 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.5 (d) 9.4
  22. 22.Best estimate of 2749 ÷ 34? (a) 9200 (b) 92 (c) 920
  23. 23.Best estimate of 2099 ÷ 63? (a) 350 (b) 3500 (c) 35
  24. 24.Best estimate of 6099 ÷ 64? (a) 102 (b) 10200 (c) 1020
  25. 25.Best estimate of 5665 ÷ 63? (a) 9400 (b) 940 (c) 94
  26. 26.Best estimate of 1209 ÷ 86? (a) 130 (b) 13 (c) 1300
  27. 27.Best estimate of 592 ÷ 49? (a) 12 (b) 120 (c) 1200
  28. 28.Best estimate of 645 ÷ 46? (a) 1300 (b) 13 (c) 130
  29. 29.√59 to 1 decimal place? (a) 7.8 (b) 7.6 (c) 7.9 (d) 7.7
  30. 30.√63 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 7.8 (d) 7.9
  31. 31.Best estimate of 1181 ÷ 32? (a) 3900 (b) 390 (c) 39
  32. 32.√52 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 7.0 (d) 6.9
  33. 33.√26 to 1 decimal place? (a) 5.3 (b) 5.1 (c) 5.2 (d) 5.0
  34. 34.Best estimate of 1714 ÷ 36? (a) 430 (b) 43 (c) 4300
  35. 35.Best estimate of 2563 ÷ 27? (a) 850 (b) 85 (c) 8500
  36. 36.Best estimate of 1399 ÷ 82? (a) 170 (b) 1700 (c) 17
  37. 37.√45 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.8 (d) 6.5
  38. 38.Best estimate of 3384 ÷ 77? (a) 420 (b) 42 (c) 4200
  39. 39.Best estimate of 1423 ÷ 48? (a) 2800 (b) 28 (c) 280
  40. 40.√22 to 1 decimal place? (a) 4.5 (b) 4.7 (c) 4.8 (d) 4.6

Answer key

  1. 7.4
  2. 13
  3. 6.1
  4. 8.1
  5. 37
  6. 8.8
  7. 9.6
  8. 5.2
  9. 25
  10. 75
  11. 34
  12. 88
  13. 8.7
  14. 6.5
  15. 75
  16. 91
  17. 8.8
  18. 5.7
  19. 71
  20. 35
  21. 9.4
  22. 92
  23. 35
  24. 102
  25. 94
  26. 13
  27. 12
  28. 13
  29. 7.7
  30. 7.9
  31. 39
  32. 7.2
  33. 5.1
  34. 43
  35. 85
  36. 17
  37. 6.7
  38. 42
  39. 28
  40. 4.7

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