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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 384 · 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 2072 ÷ 42? (a) 52 (b) 5200 (c) 520
  2. 2.√41 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.4 (d) 6.1
  3. 3.Best estimate of 1544 ÷ 71? (a) 220 (b) 22 (c) 2200
  4. 4.Best estimate of 4409 ÷ 61? (a) 7300 (b) 730 (c) 73
  5. 5.√84 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 9.1 (d) 8.9
  6. 6.Best estimate of 5808 ÷ 62? (a) 97 (b) 970 (c) 9700
  7. 7.√34 to 1 decimal place? (a) 5.5 (b) 5.8 (c) 5.7 (d) 5.6
  8. 8.Best estimate of 2137 ÷ 58? (a) 3600 (b) 36 (c) 360
  9. 9.Best estimate of 7667 ÷ 83? (a) 960 (b) 96 (c) 9600
  10. 10.Best estimate of 1183 ÷ 23? (a) 590 (b) 5900 (c) 59
  11. 11.Best estimate of 1587 ÷ 48? (a) 320 (b) 32 (c) 3200
  12. 12.Best estimate of 1068 ÷ 82? (a) 13 (b) 130 (c) 1300
  13. 13.√44 to 1 decimal place? (a) 6.8 (b) 6.6 (c) 6.5 (d) 6.7
  14. 14.√24 to 1 decimal place? (a) 4.7 (b) 4.8 (c) 4.9 (d) 4.6
  15. 15.Best estimate of 1716 ÷ 31? (a) 57 (b) 5700 (c) 570
  16. 16.Best estimate of 2347 ÷ 36? (a) 590 (b) 5900 (c) 59
  17. 17.√46 to 1 decimal place? (a) 7.1 (b) 6.8 (c) 7.0 (d) 6.9
  18. 18.Best estimate of 813 ÷ 46? (a) 160 (b) 1600 (c) 16
  19. 19.√56 to 1 decimal place? (a) 7.4 (b) 7.2 (c) 7.3 (d) 7.5
  20. 20.Best estimate of 6908 ÷ 86? (a) 7700 (b) 77 (c) 770
  21. 21.Best estimate of 1071 ÷ 24? (a) 5400 (b) 54 (c) 540
  22. 22.√23 to 1 decimal place? (a) 4.8 (b) 4.6 (c) 4.9 (d) 4.7
  23. 23.√72 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.5 (d) 8.4
  24. 24.Best estimate of 7018 ÷ 89? (a) 780 (b) 78 (c) 7800
  25. 25.√74 to 1 decimal place? (a) 8.8 (b) 8.7 (c) 8.9 (d) 8.6
  26. 26.√59 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.7 (d) 7.8
  27. 27.√43 to 1 decimal place? (a) 6.7 (b) 6.5 (c) 6.8 (d) 6.6
  28. 28.Best estimate of 1079 ÷ 49? (a) 22 (b) 2200 (c) 220
  29. 29.√40 to 1 decimal place? (a) 6.1 (b) 6.2 (c) 6.3 (d) 6.4
  30. 30.√69 to 1 decimal place? (a) 8.2 (b) 8.4 (c) 8.3 (d) 8.5
  31. 31.Best estimate of 1779 ÷ 52? (a) 360 (b) 36 (c) 3600
  32. 32.Best estimate of 3569 ÷ 66? (a) 510 (b) 5100 (c) 51
  33. 33.√55 to 1 decimal place? (a) 7.2 (b) 7.4 (c) 7.3 (d) 7.5
  34. 34.√98 to 1 decimal place? (a) 9.7 (b) 9.9 (c) 10.0 (d) 9.8
  35. 35.√78 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 9.0 (d) 8.7
  36. 36.Best estimate of 2410 ÷ 68? (a) 34 (b) 340 (c) 3400
  37. 37.Best estimate of 5865 ÷ 67? (a) 840 (b) 8400 (c) 84
  38. 38.Best estimate of 2565 ÷ 73? (a) 3700 (b) 37 (c) 370
  39. 39.Best estimate of 3194 ÷ 34? (a) 1060 (b) 106 (c) 10600
  40. 40.√82 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.3 (d) 9.0

Answer key

  1. 52
  2. 6.4
  3. 22
  4. 73
  5. 9.2
  6. 97
  7. 5.8
  8. 36
  9. 96
  10. 59
  11. 32
  12. 13
  13. 6.6
  14. 4.9
  15. 57
  16. 59
  17. 6.8
  18. 16
  19. 7.5
  20. 77
  21. 54
  22. 4.8
  23. 8.5
  24. 78
  25. 8.6
  26. 7.7
  27. 6.6
  28. 22
  29. 6.3
  30. 8.3
  31. 36
  32. 51
  33. 7.4
  34. 9.9
  35. 8.8
  36. 34
  37. 84
  38. 37
  39. 106
  40. 9.1

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