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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 864 · 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.√80 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.7 (d) 8.6
  2. 2.Best estimate of 1104 ÷ 56? (a) 1800 (b) 180 (c) 18
  3. 3.Best estimate of 653 ÷ 32? (a) 2200 (b) 220 (c) 22
  4. 4.√23 to 1 decimal place? (a) 4.7 (b) 5.0 (c) 4.9 (d) 4.8
  5. 5.Best estimate of 4949 ÷ 82? (a) 6200 (b) 620 (c) 62
  6. 6.√22 to 1 decimal place? (a) 4.8 (b) 4.5 (c) 4.6 (d) 4.7
  7. 7.√84 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.5 (d) 9.2
  8. 8.Best estimate of 3821 ÷ 47? (a) 760 (b) 7600 (c) 76
  9. 9.Best estimate of 410 ÷ 32? (a) 14 (b) 1400 (c) 140
  10. 10.√51 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 7.0 (d) 7.3
  11. 11.√31 to 1 decimal place? (a) 5.5 (b) 5.6 (c) 5.7 (d) 5.8
  12. 12.Best estimate of 1638 ÷ 66? (a) 23 (b) 2300 (c) 230
  13. 13.Best estimate of 1536 ÷ 42? (a) 3800 (b) 380 (c) 38
  14. 14.√92 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.4 (d) 9.3
  15. 15.Best estimate of 3126 ÷ 76? (a) 390 (b) 39 (c) 3900
  16. 16.√24 to 1 decimal place? (a) 4.7 (b) 5.0 (c) 4.8 (d) 4.9
  17. 17.Best estimate of 1064 ÷ 58? (a) 1800 (b) 180 (c) 18
  18. 18.Best estimate of 1099 ÷ 34? (a) 37 (b) 3700 (c) 370
  19. 19.√90 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.3 (d) 9.2
  20. 20.√26 to 1 decimal place? (a) 5.2 (b) 4.9 (c) 5.0 (d) 5.1
  21. 21.√71 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.2 (d) 8.5
  22. 22.Best estimate of 4539 ÷ 69? (a) 6500 (b) 65 (c) 650
  23. 23.√41 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.6 (d) 6.7
  24. 24.Best estimate of 4946 ÷ 62? (a) 8200 (b) 82 (c) 820
  25. 25.Best estimate of 685 ÷ 22? (a) 34 (b) 340 (c) 3400
  26. 26.Best estimate of 4621 ÷ 78? (a) 5800 (b) 580 (c) 58
  27. 27.Best estimate of 890 ÷ 72? (a) 1300 (b) 130 (c) 13
  28. 28.Best estimate of 5227 ÷ 78? (a) 65 (b) 650 (c) 6500
  29. 29.Best estimate of 2828 ÷ 32? (a) 94 (b) 940 (c) 9400
  30. 30.√53 to 1 decimal place? (a) 7.3 (b) 7.5 (c) 7.6 (d) 7.4
  31. 31.Best estimate of 3598 ÷ 84? (a) 4500 (b) 45 (c) 450
  32. 32.Best estimate of 826 ÷ 29? (a) 280 (b) 28 (c) 2800
  33. 33.√38 to 1 decimal place? (a) 6.3 (b) 6.2 (c) 6.4 (d) 6.1
  34. 34.√75 to 1 decimal place? (a) 8.7 (b) 9.0 (c) 8.9 (d) 8.8
  35. 35.Best estimate of 969 ÷ 28? (a) 3200 (b) 320 (c) 32
  36. 36.Best estimate of 6642 ÷ 82? (a) 830 (b) 8300 (c) 83
  37. 37.Best estimate of 6093 ÷ 74? (a) 87 (b) 8700 (c) 870
  38. 38.√21 to 1 decimal place? (a) 4.7 (b) 4.5 (c) 4.4 (d) 4.6
  39. 39.√27 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.5 (d) 5.2
  40. 40.√96 to 1 decimal place? (a) 10.1 (b) 9.9 (c) 9.8 (d) 10.0

Answer key

  1. 8.9
  2. 18
  3. 22
  4. 4.8
  5. 62
  6. 4.7
  7. 9.2
  8. 76
  9. 14
  10. 7.1
  11. 5.6
  12. 23
  13. 38
  14. 9.6
  15. 39
  16. 4.9
  17. 18
  18. 37
  19. 9.5
  20. 5.1
  21. 8.4
  22. 65
  23. 6.4
  24. 82
  25. 34
  26. 58
  27. 13
  28. 65
  29. 94
  30. 7.3
  31. 45
  32. 28
  33. 6.2
  34. 8.7
  35. 32
  36. 83
  37. 87
  38. 4.6
  39. 5.2
  40. 9.8

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