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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 695 · 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) 7.4 (b) 7.6 (c) 7.5 (d) 7.7
  2. 2.√22 to 1 decimal place? (a) 4.7 (b) 4.9 (c) 4.8 (d) 5.0
  3. 3.√53 to 1 decimal place? (a) 7.3 (b) 7.2 (c) 7.1 (d) 7.4
  4. 4.√43 to 1 decimal place? (a) 6.9 (b) 6.7 (c) 6.8 (d) 6.6
  5. 5.√30 to 1 decimal place? (a) 5.4 (b) 5.5 (c) 5.6 (d) 5.3
  6. 6.√28 to 1 decimal place? (a) 5.4 (b) 5.5 (c) 5.3 (d) 5.2
  7. 7.Best estimate of 1935 ÷ 83? (a) 2400 (b) 240 (c) 24
  8. 8.√94 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.4 (d) 9.7
  9. 9.√50 to 1 decimal place? (a) 6.8 (b) 7.0 (c) 6.9 (d) 7.1
  10. 10.√90 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.2 (d) 9.3
  11. 11.√24 to 1 decimal place? (a) 4.9 (b) 4.6 (c) 4.8 (d) 4.7
  12. 12.Best estimate of 546 ÷ 32? (a) 1800 (b) 180 (c) 18
  13. 13.Best estimate of 2364 ÷ 36? (a) 5900 (b) 59 (c) 590
  14. 14.Best estimate of 2596 ÷ 72? (a) 3700 (b) 370 (c) 37
  15. 15.√37 to 1 decimal place? (a) 6.0 (b) 6.1 (c) 5.8 (d) 5.9
  16. 16.√66 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.1 (d) 8.4
  17. 17.√47 to 1 decimal place? (a) 6.9 (b) 7.1 (c) 7.0 (d) 7.2
  18. 18.√86 to 1 decimal place? (a) 9.1 (b) 9.4 (c) 9.3 (d) 9.2
  19. 19.√72 to 1 decimal place? (a) 8.4 (b) 8.6 (c) 8.5 (d) 8.3
  20. 20.Best estimate of 3254 ÷ 88? (a) 36 (b) 360 (c) 3600
  21. 21.Best estimate of 1889 ÷ 82? (a) 24 (b) 2400 (c) 240
  22. 22.√78 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.5 (d) 8.8
  23. 23.Best estimate of 2957 ÷ 59? (a) 4900 (b) 490 (c) 49
  24. 24.Best estimate of 824 ÷ 66? (a) 1200 (b) 120 (c) 12
  25. 25.√96 to 1 decimal place? (a) 10.1 (b) 9.9 (c) 9.8 (d) 10.0
  26. 26.√35 to 1 decimal place? (a) 5.9 (b) 6.1 (c) 6.2 (d) 6.0
  27. 27.Best estimate of 7545 ÷ 79? (a) 940 (b) 94 (c) 9400
  28. 28.√89 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.4 (d) 9.1
  29. 29.Best estimate of 877 ÷ 71? (a) 1300 (b) 13 (c) 130
  30. 30.√26 to 1 decimal place? (a) 5.1 (b) 5.4 (c) 5.2 (d) 5.3
  31. 31.Best estimate of 1572 ÷ 48? (a) 31 (b) 310 (c) 3100
  32. 32.Best estimate of 2245 ÷ 66? (a) 3200 (b) 32 (c) 320
  33. 33.√61 to 1 decimal place? (a) 7.8 (b) 8.0 (c) 7.9 (d) 8.1
  34. 34.Best estimate of 2608 ÷ 56? (a) 430 (b) 4300 (c) 43
  35. 35.Best estimate of 2805 ÷ 32? (a) 9400 (b) 940 (c) 94
  36. 36.Best estimate of 1218 ÷ 46? (a) 240 (b) 24 (c) 2400
  37. 37.Best estimate of 1814 ÷ 69? (a) 26 (b) 260 (c) 2600
  38. 38.√74 to 1 decimal place? (a) 8.7 (b) 8.9 (c) 8.6 (d) 8.8
  39. 39.Best estimate of 4245 ÷ 56? (a) 71 (b) 7100 (c) 710
  40. 40.√58 to 1 decimal place? (a) 7.8 (b) 7.6 (c) 7.7 (d) 7.9

Answer key

  1. 7.4
  2. 4.7
  3. 7.3
  4. 6.6
  5. 5.5
  6. 5.3
  7. 24
  8. 9.7
  9. 7.1
  10. 9.5
  11. 4.9
  12. 18
  13. 59
  14. 37
  15. 6.1
  16. 8.1
  17. 6.9
  18. 9.3
  19. 8.5
  20. 36
  21. 24
  22. 8.8
  23. 49
  24. 12
  25. 9.8
  26. 5.9
  27. 94
  28. 9.4
  29. 13
  30. 5.1
  31. 31
  32. 32
  33. 7.8
  34. 43
  35. 94
  36. 24
  37. 26
  38. 8.6
  39. 71
  40. 7.6

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