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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 112 · 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.√77 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.6 (d) 8.9
  2. 2.Best estimate of 1733 ÷ 32? (a) 58 (b) 5800 (c) 580
  3. 3.√34 to 1 decimal place? (a) 5.8 (b) 6.1 (c) 5.9 (d) 6.0
  4. 4.Best estimate of 3445 ÷ 79? (a) 430 (b) 4300 (c) 43
  5. 5.√52 to 1 decimal place? (a) 7.4 (b) 7.1 (c) 7.3 (d) 7.2
  6. 6.√35 to 1 decimal place? (a) 6.1 (b) 5.9 (c) 6.0 (d) 5.8
  7. 7.√28 to 1 decimal place? (a) 5.2 (b) 5.3 (c) 5.0 (d) 5.1
  8. 8.√48 to 1 decimal place? (a) 6.9 (b) 6.6 (c) 6.7 (d) 6.8
  9. 9.Best estimate of 1161 ÷ 72? (a) 1700 (b) 170 (c) 17
  10. 10.√29 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.6 (d) 5.5
  11. 11.√26 to 1 decimal place? (a) 5.1 (b) 5.4 (c) 5.2 (d) 5.3
  12. 12.√96 to 1 decimal place? (a) 9.9 (b) 9.8 (c) 10.1 (d) 10.0
  13. 13.Best estimate of 4133 ÷ 89? (a) 4600 (b) 46 (c) 460
  14. 14.Best estimate of 870 ÷ 32? (a) 29 (b) 290 (c) 2900
  15. 15.√80 to 1 decimal place? (a) 8.9 (b) 8.6 (c) 8.8 (d) 8.7
  16. 16.Best estimate of 2059 ÷ 64? (a) 34 (b) 3400 (c) 340
  17. 17.Best estimate of 599 ÷ 21? (a) 300 (b) 3000 (c) 30
  18. 18.Best estimate of 494 ÷ 38? (a) 1200 (b) 12 (c) 120
  19. 19.Best estimate of 2902 ÷ 46? (a) 58 (b) 580 (c) 5800
  20. 20.√40 to 1 decimal place? (a) 6.4 (b) 6.6 (c) 6.3 (d) 6.5
  21. 21.Best estimate of 1865 ÷ 44? (a) 4700 (b) 47 (c) 470
  22. 22.Best estimate of 2257 ÷ 47? (a) 450 (b) 45 (c) 4500
  23. 23.Best estimate of 2200 ÷ 39? (a) 550 (b) 5500 (c) 55
  24. 24.Best estimate of 2771 ÷ 56? (a) 460 (b) 46 (c) 4600
  25. 25.Best estimate of 4012 ÷ 81? (a) 50 (b) 500 (c) 5000
  26. 26.√37 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.1 (d) 6.0
  27. 27.Best estimate of 1141 ÷ 88? (a) 130 (b) 1300 (c) 13
  28. 28.Best estimate of 2535 ÷ 68? (a) 3600 (b) 36 (c) 360
  29. 29.Best estimate of 2233 ÷ 72? (a) 320 (b) 32 (c) 3200
  30. 30.√74 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.5 (d) 8.4
  31. 31.Best estimate of 2826 ÷ 64? (a) 470 (b) 47 (c) 4700
  32. 32.√44 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 6.7 (d) 6.6
  33. 33.Best estimate of 6392 ÷ 76? (a) 8000 (b) 800 (c) 80
  34. 34.Best estimate of 5536 ÷ 87? (a) 6200 (b) 62 (c) 620
  35. 35.Best estimate of 992 ÷ 32? (a) 33 (b) 330 (c) 3300
  36. 36.√21 to 1 decimal place? (a) 4.7 (b) 4.5 (c) 4.6 (d) 4.4
  37. 37.√58 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.4 (d) 7.3
  38. 38.√82 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.2 (d) 9.1
  39. 39.√46 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 7.1 (d) 7.0
  40. 40.Best estimate of 5487 ÷ 66? (a) 78 (b) 7800 (c) 780

Answer key

  1. 8.8
  2. 58
  3. 5.8
  4. 43
  5. 7.2
  6. 5.9
  7. 5.3
  8. 6.9
  9. 17
  10. 5.4
  11. 5.1
  12. 9.8
  13. 46
  14. 29
  15. 8.9
  16. 34
  17. 30
  18. 12
  19. 58
  20. 6.3
  21. 47
  22. 45
  23. 55
  24. 46
  25. 50
  26. 6.1
  27. 13
  28. 36
  29. 32
  30. 8.6
  31. 47
  32. 6.6
  33. 80
  34. 62
  35. 33
  36. 4.6
  37. 7.6
  38. 9.1
  39. 6.8
  40. 78

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