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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 197 · 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 1158 ÷ 28? (a) 390 (b) 39 (c) 3900
  2. 2.Best estimate of 1944 ÷ 72? (a) 280 (b) 2800 (c) 28
  3. 3.Best estimate of 1029 ÷ 26? (a) 340 (b) 3400 (c) 34
  4. 4.Best estimate of 5856 ÷ 66? (a) 84 (b) 8400 (c) 840
  5. 5.√85 to 1 decimal place? (a) 9.5 (b) 9.3 (c) 9.2 (d) 9.4
  6. 6.√72 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.4 (d) 8.7
  7. 7.Best estimate of 1315 ÷ 51? (a) 26 (b) 260 (c) 2600
  8. 8.√29 to 1 decimal place? (a) 5.6 (b) 5.4 (c) 5.5 (d) 5.7
  9. 9.Best estimate of 3300 ÷ 44? (a) 8300 (b) 830 (c) 83
  10. 10.Best estimate of 2211 ÷ 87? (a) 250 (b) 2500 (c) 25
  11. 11.Best estimate of 4420 ÷ 62? (a) 7400 (b) 74 (c) 740
  12. 12.Best estimate of 3960 ÷ 52? (a) 79 (b) 7900 (c) 790
  13. 13.√51 to 1 decimal place? (a) 7.2 (b) 7.3 (c) 7.1 (d) 7.4
  14. 14.√71 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.2 (d) 8.5
  15. 15.√96 to 1 decimal place? (a) 9.8 (b) 10.1 (c) 9.9 (d) 10.0
  16. 16.Best estimate of 1043 ÷ 33? (a) 35 (b) 3500 (c) 350
  17. 17.Best estimate of 4713 ÷ 84? (a) 590 (b) 59 (c) 5900
  18. 18.√31 to 1 decimal place? (a) 5.5 (b) 5.6 (c) 5.8 (d) 5.7
  19. 19.Best estimate of 1642 ÷ 44? (a) 4100 (b) 410 (c) 41
  20. 20.√26 to 1 decimal place? (a) 5.1 (b) 5.3 (c) 5.2 (d) 5.0
  21. 21.√44 to 1 decimal place? (a) 6.5 (b) 6.7 (c) 6.8 (d) 6.6
  22. 22.Best estimate of 3097 ÷ 87? (a) 3400 (b) 34 (c) 340
  23. 23.√21 to 1 decimal place? (a) 4.6 (b) 4.7 (c) 4.8 (d) 4.5
  24. 24.Best estimate of 710 ÷ 39? (a) 1800 (b) 18 (c) 180
  25. 25.Best estimate of 470 ÷ 39? (a) 120 (b) 1200 (c) 12
  26. 26.Best estimate of 4725 ÷ 56? (a) 790 (b) 7900 (c) 79
  27. 27.Best estimate of 5308 ÷ 88? (a) 59 (b) 590 (c) 5900
  28. 28.Best estimate of 1247 ÷ 23? (a) 620 (b) 6200 (c) 62
  29. 29.√90 to 1 decimal place? (a) 9.6 (b) 9.5 (c) 9.3 (d) 9.4
  30. 30.√75 to 1 decimal place? (a) 8.8 (b) 8.7 (c) 8.9 (d) 9.0
  31. 31.√53 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.4 (d) 7.3
  32. 32.√35 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 6.0 (d) 5.9
  33. 33.Best estimate of 1259 ÷ 76? (a) 1600 (b) 160 (c) 16
  34. 34.Best estimate of 3360 ÷ 87? (a) 370 (b) 37 (c) 3700
  35. 35.√69 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.3 (d) 8.4
  36. 36.√98 to 1 decimal place? (a) 10.0 (b) 10.2 (c) 10.1 (d) 9.9
  37. 37.Best estimate of 1941 ÷ 23? (a) 970 (b) 9700 (c) 97
  38. 38.Best estimate of 4104 ÷ 44? (a) 10300 (b) 103 (c) 1030
  39. 39.Best estimate of 1775 ÷ 72? (a) 250 (b) 2500 (c) 25
  40. 40.√87 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.3 (d) 9.6

Answer key

  1. 39
  2. 28
  3. 34
  4. 84
  5. 9.2
  6. 8.5
  7. 26
  8. 5.4
  9. 83
  10. 25
  11. 74
  12. 79
  13. 7.1
  14. 8.4
  15. 9.8
  16. 35
  17. 59
  18. 5.6
  19. 41
  20. 5.1
  21. 6.6
  22. 34
  23. 4.6
  24. 18
  25. 12
  26. 79
  27. 59
  28. 62
  29. 9.5
  30. 8.7
  31. 7.3
  32. 5.9
  33. 16
  34. 37
  35. 8.3
  36. 9.9
  37. 97
  38. 103
  39. 25
  40. 9.3

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