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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 257 · 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 3911 ÷ 78? (a) 49 (b) 4900 (c) 490
  2. 2.Best estimate of 1074 ÷ 22? (a) 54 (b) 5400 (c) 540
  3. 3.√72 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.2 (d) 8.3
  4. 4.Best estimate of 5653 ÷ 74? (a) 8100 (b) 810 (c) 81
  5. 5.√34 to 1 decimal place? (a) 6.0 (b) 5.8 (c) 5.9 (d) 5.7
  6. 6.Best estimate of 6600 ÷ 69? (a) 940 (b) 94 (c) 9400
  7. 7.√92 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.4 (d) 9.5
  8. 8.Best estimate of 3560 ÷ 56? (a) 59 (b) 5900 (c) 590
  9. 9.Best estimate of 3480 ÷ 54? (a) 700 (b) 7000 (c) 70
  10. 10.√52 to 1 decimal place? (a) 7.2 (b) 7.5 (c) 7.4 (d) 7.3
  11. 11.√70 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.4 (d) 8.1
  12. 12.Best estimate of 583 ÷ 31? (a) 1900 (b) 19 (c) 190
  13. 13.√77 to 1 decimal place? (a) 9.1 (b) 8.8 (c) 8.9 (d) 9.0
  14. 14.√98 to 1 decimal place? (a) 10.2 (b) 10.1 (c) 9.9 (d) 10.0
  15. 15.Best estimate of 1125 ÷ 37? (a) 280 (b) 28 (c) 2800
  16. 16.√26 to 1 decimal place? (a) 5.2 (b) 5.1 (c) 5.3 (d) 5.0
  17. 17.√40 to 1 decimal place? (a) 6.5 (b) 6.3 (c) 6.4 (d) 6.2
  18. 18.√55 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.3 (d) 7.6
  19. 19.Best estimate of 3312 ÷ 52? (a) 6600 (b) 66 (c) 660
  20. 20.Best estimate of 2200 ÷ 23? (a) 11000 (b) 1100 (c) 110
  21. 21.Best estimate of 3096 ÷ 52? (a) 620 (b) 6200 (c) 62
  22. 22.Best estimate of 4496 ÷ 72? (a) 6400 (b) 64 (c) 640
  23. 23.√74 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.9 (d) 8.8
  24. 24.Best estimate of 4938 ÷ 89? (a) 550 (b) 5500 (c) 55
  25. 25.Best estimate of 911 ÷ 34? (a) 3000 (b) 30 (c) 300
  26. 26.√82 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.4 (d) 9.1
  27. 27.Best estimate of 2009 ÷ 49? (a) 4000 (b) 400 (c) 40
  28. 28.Best estimate of 1726 ÷ 51? (a) 350 (b) 35 (c) 3500
  29. 29.√53 to 1 decimal place? (a) 7.5 (b) 7.3 (c) 7.2 (d) 7.4
  30. 30.Best estimate of 1753 ÷ 42? (a) 4400 (b) 44 (c) 440
  31. 31.√69 to 1 decimal place? (a) 8.4 (b) 8.2 (c) 8.3 (d) 8.5
  32. 32.Best estimate of 8236 ÷ 87? (a) 920 (b) 9200 (c) 92
  33. 33.Best estimate of 5869 ÷ 72? (a) 84 (b) 840 (c) 8400
  34. 34.Best estimate of 1253 ÷ 53? (a) 25 (b) 250 (c) 2500
  35. 35.√23 to 1 decimal place? (a) 4.5 (b) 4.7 (c) 4.6 (d) 4.8
  36. 36.√65 to 1 decimal place? (a) 8.1 (b) 8.3 (c) 8.4 (d) 8.2
  37. 37.Best estimate of 3524 ÷ 72? (a) 500 (b) 50 (c) 5000
  38. 38.√38 to 1 decimal place? (a) 6.5 (b) 6.2 (c) 6.4 (d) 6.3
  39. 39.Best estimate of 1689 ÷ 53? (a) 3400 (b) 34 (c) 340
  40. 40.Best estimate of 688 ÷ 49? (a) 140 (b) 14 (c) 1400

Answer key

  1. 49
  2. 54
  3. 8.5
  4. 81
  5. 5.8
  6. 94
  7. 9.6
  8. 59
  9. 70
  10. 7.2
  11. 8.4
  12. 19
  13. 8.8
  14. 9.9
  15. 28
  16. 5.1
  17. 6.3
  18. 7.4
  19. 66
  20. 110
  21. 62
  22. 64
  23. 8.6
  24. 55
  25. 30
  26. 9.1
  27. 40
  28. 35
  29. 7.3
  30. 44
  31. 8.3
  32. 92
  33. 84
  34. 25
  35. 4.8
  36. 8.1
  37. 50
  38. 6.2
  39. 34
  40. 14

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