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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 158 · 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.√55 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 7.4 (d) 7.3
  2. 2.√62 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 7.6 (d) 7.9
  3. 3.√72 to 1 decimal place? (a) 8.4 (b) 8.7 (c) 8.6 (d) 8.5
  4. 4.√47 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.9 (d) 6.8
  5. 5.√46 to 1 decimal place? (a) 6.6 (b) 6.9 (c) 6.8 (d) 6.7
  6. 6.Best estimate of 2029 ÷ 52? (a) 4100 (b) 41 (c) 410
  7. 7.Best estimate of 5763 ÷ 71? (a) 820 (b) 8200 (c) 82
  8. 8.Best estimate of 1191 ÷ 61? (a) 2000 (b) 20 (c) 200
  9. 9.√24 to 1 decimal place? (a) 5.1 (b) 5.2 (c) 5.0 (d) 4.9
  10. 10.Best estimate of 4464 ÷ 57? (a) 74 (b) 7400 (c) 740
  11. 11.Best estimate of 4573 ÷ 56? (a) 760 (b) 76 (c) 7600
  12. 12.Best estimate of 1682 ÷ 26? (a) 56 (b) 5600 (c) 560
  13. 13.Best estimate of 2594 ÷ 31? (a) 86 (b) 8600 (c) 860
  14. 14.Best estimate of 5100 ÷ 77? (a) 640 (b) 6400 (c) 64
  15. 15.Best estimate of 1916 ÷ 62? (a) 320 (b) 32 (c) 3200
  16. 16.Best estimate of 2117 ÷ 33? (a) 71 (b) 7100 (c) 710
  17. 17.√88 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.5 (d) 9.3
  18. 18.Best estimate of 1957 ÷ 31? (a) 65 (b) 6500 (c) 650
  19. 19.Best estimate of 2638 ÷ 52? (a) 5300 (b) 53 (c) 530
  20. 20.Best estimate of 7708 ÷ 81? (a) 9600 (b) 96 (c) 960
  21. 21.Best estimate of 3655 ÷ 46? (a) 730 (b) 7300 (c) 73
  22. 22.√30 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.5 (d) 5.2
  23. 23.Best estimate of 1373 ÷ 73? (a) 2000 (b) 200 (c) 20
  24. 24.Best estimate of 1534 ÷ 27? (a) 510 (b) 51 (c) 5100
  25. 25.Best estimate of 4196 ÷ 46? (a) 8400 (b) 84 (c) 840
  26. 26.√89 to 1 decimal place? (a) 9.4 (b) 9.6 (c) 9.7 (d) 9.5
  27. 27.Best estimate of 3753 ÷ 56? (a) 630 (b) 6300 (c) 63
  28. 28.√34 to 1 decimal place? (a) 5.7 (b) 5.5 (c) 5.8 (d) 5.6
  29. 29.√32 to 1 decimal place? (a) 5.8 (b) 5.6 (c) 5.5 (d) 5.7
  30. 30.Best estimate of 6898 ÷ 81? (a) 8600 (b) 86 (c) 860
  31. 31.√69 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.1 (d) 8.4
  32. 32.√59 to 1 decimal place? (a) 8.0 (b) 7.8 (c) 7.7 (d) 7.9
  33. 33.Best estimate of 924 ÷ 58? (a) 150 (b) 1500 (c) 15
  34. 34.Best estimate of 2353 ÷ 31? (a) 78 (b) 780 (c) 7800
  35. 35.√98 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 9.9 (d) 10.0
  36. 36.Best estimate of 6273 ÷ 82? (a) 780 (b) 78 (c) 7800
  37. 37.Best estimate of 3116 ÷ 84? (a) 3900 (b) 390 (c) 39
  38. 38.Best estimate of 846 ÷ 22? (a) 420 (b) 42 (c) 4200
  39. 39.Best estimate of 1959 ÷ 34? (a) 6500 (b) 65 (c) 650
  40. 40.√63 to 1 decimal place? (a) 7.7 (b) 7.9 (c) 8.0 (d) 7.8

Answer key

  1. 7.4
  2. 7.9
  3. 8.5
  4. 6.9
  5. 6.8
  6. 41
  7. 82
  8. 20
  9. 4.9
  10. 74
  11. 76
  12. 56
  13. 86
  14. 64
  15. 32
  16. 71
  17. 9.4
  18. 65
  19. 53
  20. 96
  21. 73
  22. 5.5
  23. 20
  24. 51
  25. 84
  26. 9.4
  27. 63
  28. 5.8
  29. 5.7
  30. 86
  31. 8.3
  32. 7.7
  33. 15
  34. 78
  35. 9.9
  36. 78
  37. 39
  38. 42
  39. 65
  40. 7.9

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