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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 723 · 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.√98 to 1 decimal place? (a) 9.7 (b) 9.9 (c) 9.8 (d) 9.6
  2. 2.√22 to 1 decimal place? (a) 4.9 (b) 5.0 (c) 4.7 (d) 4.8
  3. 3.Best estimate of 2725 ÷ 56? (a) 450 (b) 4500 (c) 45
  4. 4.Best estimate of 4895 ÷ 61? (a) 8200 (b) 82 (c) 820
  5. 5.Best estimate of 6535 ÷ 73? (a) 9300 (b) 93 (c) 930
  6. 6.Best estimate of 3544 ÷ 49? (a) 71 (b) 710 (c) 7100
  7. 7.Best estimate of 1959 ÷ 33? (a) 65 (b) 6500 (c) 650
  8. 8.√53 to 1 decimal place? (a) 7.4 (b) 7.6 (c) 7.3 (d) 7.5
  9. 9.Best estimate of 2765 ÷ 76? (a) 350 (b) 35 (c) 3500
  10. 10.Best estimate of 5717 ÷ 87? (a) 6400 (b) 640 (c) 64
  11. 11.Best estimate of 1065 ÷ 46? (a) 21 (b) 210 (c) 2100
  12. 12.Best estimate of 5888 ÷ 62? (a) 98 (b) 980 (c) 9800
  13. 13.Best estimate of 3407 ÷ 89? (a) 38 (b) 380 (c) 3800
  14. 14.Best estimate of 320 ÷ 23? (a) 160 (b) 1600 (c) 16
  15. 15.Best estimate of 961 ÷ 37? (a) 24 (b) 2400 (c) 240
  16. 16.Best estimate of 1870 ÷ 21? (a) 94 (b) 940 (c) 9400
  17. 17.√59 to 1 decimal place? (a) 7.7 (b) 7.5 (c) 7.4 (d) 7.6
  18. 18.√63 to 1 decimal place? (a) 7.9 (b) 8.1 (c) 8.0 (d) 7.8
  19. 19.Best estimate of 6944 ÷ 79? (a) 870 (b) 8700 (c) 87
  20. 20.√34 to 1 decimal place? (a) 5.7 (b) 6.0 (c) 5.8 (d) 5.9
  21. 21.Best estimate of 1851 ÷ 52? (a) 370 (b) 3700 (c) 37
  22. 22.√38 to 1 decimal place? (a) 6.1 (b) 6.2 (c) 6.3 (d) 6.0
  23. 23.Best estimate of 3554 ÷ 82? (a) 44 (b) 4400 (c) 440
  24. 24.√62 to 1 decimal place? (a) 7.8 (b) 8.0 (c) 7.9 (d) 7.7
  25. 25.√45 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.6 (d) 6.9
  26. 26.Best estimate of 4552 ÷ 83? (a) 5700 (b) 570 (c) 57
  27. 27.Best estimate of 988 ÷ 32? (a) 33 (b) 330 (c) 3300
  28. 28.Best estimate of 4199 ÷ 57? (a) 700 (b) 70 (c) 7000
  29. 29.√52 to 1 decimal place? (a) 7.1 (b) 7.3 (c) 7.0 (d) 7.2
  30. 30.Best estimate of 1075 ÷ 24? (a) 5400 (b) 540 (c) 54
  31. 31.Best estimate of 1510 ÷ 22? (a) 760 (b) 7600 (c) 76
  32. 32.Best estimate of 8388 ÷ 89? (a) 9300 (b) 930 (c) 93
  33. 33.√74 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.4 (d) 8.3
  34. 34.√37 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 5.9 (d) 6.0
  35. 35.Best estimate of 2018 ÷ 56? (a) 3400 (b) 34 (c) 340
  36. 36.Best estimate of 4998 ÷ 89? (a) 56 (b) 560 (c) 5600
  37. 37.√92 to 1 decimal place? (a) 9.9 (b) 9.6 (c) 9.8 (d) 9.7
  38. 38.√67 to 1 decimal place? (a) 8.3 (b) 8.5 (c) 8.2 (d) 8.4
  39. 39.√56 to 1 decimal place? (a) 7.5 (b) 7.3 (c) 7.2 (d) 7.4
  40. 40.Best estimate of 2499 ÷ 47? (a) 5000 (b) 50 (c) 500

Answer key

  1. 9.9
  2. 4.7
  3. 45
  4. 82
  5. 93
  6. 71
  7. 65
  8. 7.3
  9. 35
  10. 64
  11. 21
  12. 98
  13. 38
  14. 16
  15. 24
  16. 94
  17. 7.7
  18. 7.9
  19. 87
  20. 5.8
  21. 37
  22. 6.2
  23. 44
  24. 7.9
  25. 6.7
  26. 57
  27. 33
  28. 70
  29. 7.2
  30. 54
  31. 76
  32. 93
  33. 8.6
  34. 6.1
  35. 34
  36. 56
  37. 9.6
  38. 8.2
  39. 7.5
  40. 50

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