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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 300 · 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.√67 to 1 decimal place? (a) 8.3 (b) 8.5 (c) 8.4 (d) 8.2
  2. 2.√98 to 1 decimal place? (a) 10.0 (b) 9.8 (c) 9.9 (d) 10.1
  3. 3.√28 to 1 decimal place? (a) 5.5 (b) 5.3 (c) 5.2 (d) 5.4
  4. 4.√89 to 1 decimal place? (a) 9.4 (b) 9.2 (c) 9.1 (d) 9.3
  5. 5.Best estimate of 476 ÷ 22? (a) 240 (b) 24 (c) 2400
  6. 6.Best estimate of 1296 ÷ 56? (a) 22 (b) 220 (c) 2200
  7. 7.√53 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 7.0 (d) 7.3
  8. 8.Best estimate of 2189 ÷ 41? (a) 5500 (b) 550 (c) 55
  9. 9.√22 to 1 decimal place? (a) 4.4 (b) 4.7 (c) 4.5 (d) 4.6
  10. 10.Best estimate of 2000 ÷ 61? (a) 33 (b) 3300 (c) 330
  11. 11.√69 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.0 (d) 8.1
  12. 12.√35 to 1 decimal place? (a) 5.8 (b) 6.1 (c) 5.9 (d) 6.0
  13. 13.Best estimate of 969 ÷ 52? (a) 190 (b) 1900 (c) 19
  14. 14.√92 to 1 decimal place? (a) 9.5 (b) 9.3 (c) 9.6 (d) 9.4
  15. 15.Best estimate of 532 ÷ 28? (a) 1800 (b) 180 (c) 18
  16. 16.√29 to 1 decimal place? (a) 5.3 (b) 5.1 (c) 5.4 (d) 5.2
  17. 17.Best estimate of 2180 ÷ 72? (a) 3100 (b) 31 (c) 310
  18. 18.Best estimate of 1871 ÷ 79? (a) 23 (b) 2300 (c) 230
  19. 19.√66 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 7.9 (d) 8.0
  20. 20.√23 to 1 decimal place? (a) 4.9 (b) 4.6 (c) 4.7 (d) 4.8
  21. 21.Best estimate of 5777 ÷ 86? (a) 6400 (b) 640 (c) 64
  22. 22.Best estimate of 1629 ÷ 26? (a) 540 (b) 5400 (c) 54
  23. 23.Best estimate of 1936 ÷ 56? (a) 3200 (b) 32 (c) 320
  24. 24.Best estimate of 1560 ÷ 39? (a) 3900 (b) 390 (c) 39
  25. 25.Best estimate of 3590 ÷ 42? (a) 9000 (b) 90 (c) 900
  26. 26.√80 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 8.7 (d) 8.8
  27. 27.Best estimate of 2203 ÷ 39? (a) 5500 (b) 550 (c) 55
  28. 28.Best estimate of 1096 ÷ 77? (a) 1400 (b) 140 (c) 14
  29. 29.Best estimate of 4850 ÷ 82? (a) 6100 (b) 610 (c) 61
  30. 30.Best estimate of 1472 ÷ 83? (a) 180 (b) 1800 (c) 18
  31. 31.Best estimate of 5151 ÷ 62? (a) 86 (b) 860 (c) 8600
  32. 32.Best estimate of 1867 ÷ 26? (a) 62 (b) 6200 (c) 620
  33. 33.Best estimate of 1022 ÷ 31? (a) 340 (b) 34 (c) 3400
  34. 34.Best estimate of 3768 ÷ 59? (a) 6300 (b) 63 (c) 630
  35. 35.√21 to 1 decimal place? (a) 4.7 (b) 4.8 (c) 4.6 (d) 4.5
  36. 36.Best estimate of 2778 ÷ 52? (a) 560 (b) 5600 (c) 56
  37. 37.√82 to 1 decimal place? (a) 9.2 (b) 8.9 (c) 9.1 (d) 9.0
  38. 38.√46 to 1 decimal place? (a) 6.8 (b) 6.6 (c) 6.5 (d) 6.7
  39. 39.Best estimate of 592 ÷ 29? (a) 2000 (b) 200 (c) 20
  40. 40.Best estimate of 7839 ÷ 86? (a) 870 (b) 8700 (c) 87

Answer key

  1. 8.2
  2. 9.9
  3. 5.3
  4. 9.4
  5. 24
  6. 22
  7. 7.3
  8. 55
  9. 4.7
  10. 33
  11. 8.3
  12. 5.9
  13. 19
  14. 9.6
  15. 18
  16. 5.4
  17. 31
  18. 23
  19. 8.1
  20. 4.8
  21. 64
  22. 54
  23. 32
  24. 39
  25. 90
  26. 8.9
  27. 55
  28. 14
  29. 61
  30. 18
  31. 86
  32. 62
  33. 34
  34. 63
  35. 4.6
  36. 56
  37. 9.1
  38. 6.8
  39. 20
  40. 87

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