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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 252 · 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.√84 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.5 (d) 9.2
  2. 2.Best estimate of 2853 ÷ 33? (a) 950 (b) 9500 (c) 95
  3. 3.√79 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 8.9 (d) 9.0
  4. 4.Best estimate of 2427 ÷ 73? (a) 350 (b) 35 (c) 3500
  5. 5.√42 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.2 (d) 6.3
  6. 6.√67 to 1 decimal place? (a) 7.9 (b) 8.2 (c) 8.0 (d) 8.1
  7. 7.√98 to 1 decimal place? (a) 9.6 (b) 9.9 (c) 9.7 (d) 9.8
  8. 8.√40 to 1 decimal place? (a) 6.0 (b) 6.1 (c) 6.2 (d) 6.3
  9. 9.√94 to 1 decimal place? (a) 9.9 (b) 10.0 (c) 9.8 (d) 9.7
  10. 10.√75 to 1 decimal place? (a) 8.7 (b) 9.0 (c) 8.8 (d) 8.9
  11. 11.√50 to 1 decimal place? (a) 7.2 (b) 7.4 (c) 7.3 (d) 7.1
  12. 12.√92 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.3 (d) 9.4
  13. 13.Best estimate of 5338 ÷ 71? (a) 7600 (b) 760 (c) 76
  14. 14.√56 to 1 decimal place? (a) 7.2 (b) 7.4 (c) 7.3 (d) 7.5
  15. 15.√30 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.5 (d) 5.6
  16. 16.√70 to 1 decimal place? (a) 8.2 (b) 8.4 (c) 8.3 (d) 8.1
  17. 17.√47 to 1 decimal place? (a) 6.7 (b) 6.9 (c) 7.0 (d) 6.8
  18. 18.Best estimate of 1750 ÷ 76? (a) 22 (b) 2200 (c) 220
  19. 19.√74 to 1 decimal place? (a) 8.4 (b) 8.6 (c) 8.3 (d) 8.5
  20. 20.Best estimate of 2372 ÷ 56? (a) 4000 (b) 40 (c) 400
  21. 21.Best estimate of 4001 ÷ 58? (a) 670 (b) 67 (c) 6700
  22. 22.√20 to 1 decimal place? (a) 4.3 (b) 4.4 (c) 4.2 (d) 4.5
  23. 23.√23 to 1 decimal place? (a) 4.7 (b) 4.8 (c) 4.9 (d) 4.6
  24. 24.√46 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 6.7 (d) 7.0
  25. 25.Best estimate of 512 ÷ 23? (a) 26 (b) 260 (c) 2600
  26. 26.Best estimate of 2852 ÷ 46? (a) 570 (b) 5700 (c) 57
  27. 27.√76 to 1 decimal place? (a) 8.8 (b) 9.0 (c) 8.9 (d) 8.7
  28. 28.√55 to 1 decimal place? (a) 7.2 (b) 7.4 (c) 7.1 (d) 7.3
  29. 29.√26 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.4 (d) 5.1
  30. 30.Best estimate of 4669 ÷ 79? (a) 5800 (b) 580 (c) 58
  31. 31.√61 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 8.1 (d) 8.0
  32. 32.Best estimate of 6456 ÷ 69? (a) 9200 (b) 920 (c) 92
  33. 33.Best estimate of 3499 ÷ 42? (a) 870 (b) 8700 (c) 87
  34. 34.Best estimate of 659 ÷ 54? (a) 1300 (b) 13 (c) 130
  35. 35.√59 to 1 decimal place? (a) 7.6 (b) 7.4 (c) 7.7 (d) 7.5
  36. 36.Best estimate of 1176 ÷ 39? (a) 290 (b) 29 (c) 2900
  37. 37.√52 to 1 decimal place? (a) 7.3 (b) 7.5 (c) 7.4 (d) 7.2
  38. 38.Best estimate of 7737 ÷ 82? (a) 970 (b) 9700 (c) 97
  39. 39.Best estimate of 5064 ÷ 82? (a) 63 (b) 6300 (c) 630
  40. 40.Best estimate of 690 ÷ 32? (a) 2300 (b) 230 (c) 23

Answer key

  1. 9.2
  2. 95
  3. 8.9
  4. 35
  5. 6.5
  6. 8.2
  7. 9.9
  8. 6.3
  9. 9.7
  10. 8.7
  11. 7.1
  12. 9.6
  13. 76
  14. 7.5
  15. 5.5
  16. 8.4
  17. 6.9
  18. 22
  19. 8.6
  20. 40
  21. 67
  22. 4.5
  23. 4.8
  24. 6.8
  25. 26
  26. 57
  27. 8.7
  28. 7.4
  29. 5.1
  30. 58
  31. 7.8
  32. 92
  33. 87
  34. 13
  35. 7.7
  36. 29
  37. 7.2
  38. 97
  39. 63
  40. 23

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