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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 209 · 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.Best estimate of 2109 ÷ 62? (a) 350 (b) 35 (c) 3500
  2. 2.Best estimate of 1313 ÷ 26? (a) 440 (b) 4400 (c) 44
  3. 3.√53 to 1 decimal place? (a) 7.3 (b) 7.5 (c) 7.4 (d) 7.2
  4. 4.√26 to 1 decimal place? (a) 5.0 (b) 5.1 (c) 4.9 (d) 5.2
  5. 5.Best estimate of 1447 ÷ 82? (a) 18 (b) 180 (c) 1800
  6. 6.√67 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 7.9 (d) 8.0
  7. 7.Best estimate of 3907 ÷ 42? (a) 980 (b) 98 (c) 9800
  8. 8.√56 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.3 (d) 7.2
  9. 9.√62 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 8.2 (d) 7.9
  10. 10.√87 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.5 (d) 9.6
  11. 11.Best estimate of 2691 ÷ 86? (a) 3000 (b) 30 (c) 300
  12. 12.√22 to 1 decimal place? (a) 5.0 (b) 4.7 (c) 4.8 (d) 4.9
  13. 13.Best estimate of 1956 ÷ 24? (a) 9800 (b) 980 (c) 98
  14. 14.Best estimate of 3973 ÷ 68? (a) 5700 (b) 57 (c) 570
  15. 15.√23 to 1 decimal place? (a) 4.6 (b) 4.8 (c) 4.5 (d) 4.7
  16. 16.Best estimate of 494 ÷ 26? (a) 160 (b) 1600 (c) 16
  17. 17.√89 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 9.4 (d) 9.3
  18. 18.Best estimate of 1688 ÷ 34? (a) 560 (b) 5600 (c) 56
  19. 19.√32 to 1 decimal place? (a) 5.6 (b) 5.5 (c) 5.7 (d) 5.8
  20. 20.√96 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.7 (d) 9.8
  21. 21.√55 to 1 decimal place? (a) 7.6 (b) 7.4 (c) 7.7 (d) 7.5
  22. 22.Best estimate of 2654 ÷ 86? (a) 290 (b) 2900 (c) 29
  23. 23.Best estimate of 943 ÷ 28? (a) 31 (b) 3100 (c) 310
  24. 24.√65 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 8.0 (d) 8.1
  25. 25.Best estimate of 1539 ÷ 34? (a) 510 (b) 5100 (c) 51
  26. 26.Best estimate of 1026 ÷ 32? (a) 34 (b) 340 (c) 3400
  27. 27.√69 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.3 (d) 8.4
  28. 28.Best estimate of 3434 ÷ 36? (a) 8600 (b) 86 (c) 860
  29. 29.Best estimate of 1765 ÷ 78? (a) 220 (b) 22 (c) 2200
  30. 30.Best estimate of 4028 ÷ 52? (a) 8100 (b) 810 (c) 81
  31. 31.Best estimate of 2973 ÷ 73? (a) 42 (b) 420 (c) 4200
  32. 32.Best estimate of 1962 ÷ 28? (a) 6500 (b) 65 (c) 650
  33. 33.√61 to 1 decimal place? (a) 7.8 (b) 8.1 (c) 8.0 (d) 7.9
  34. 34.Best estimate of 2660 ÷ 39? (a) 670 (b) 6700 (c) 67
  35. 35.√82 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 9.3 (d) 9.2
  36. 36.Best estimate of 4178 ÷ 78? (a) 5200 (b) 520 (c) 52
  37. 37.Best estimate of 3408 ÷ 87? (a) 38 (b) 3800 (c) 380
  38. 38.√94 to 1 decimal place? (a) 9.6 (b) 9.8 (c) 9.7 (d) 9.5
  39. 39.Best estimate of 6818 ÷ 87? (a) 760 (b) 7600 (c) 76
  40. 40.√58 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 7.6 (d) 7.5

Answer key

  1. 35
  2. 44
  3. 7.3
  4. 5.1
  5. 18
  6. 8.2
  7. 98
  8. 7.5
  9. 7.9
  10. 9.3
  11. 30
  12. 4.7
  13. 98
  14. 57
  15. 4.8
  16. 16
  17. 9.4
  18. 56
  19. 5.7
  20. 9.8
  21. 7.4
  22. 29
  23. 31
  24. 8.1
  25. 51
  26. 34
  27. 8.3
  28. 86
  29. 22
  30. 81
  31. 42
  32. 65
  33. 7.8
  34. 67
  35. 9.1
  36. 52
  37. 38
  38. 9.7
  39. 76
  40. 7.6

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