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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 412 · 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.√34 to 1 decimal place? (a) 6.0 (b) 5.8 (c) 5.9 (d) 5.7
  2. 2.√88 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.4 (d) 9.5
  3. 3.Best estimate of 3012 ÷ 42? (a) 75 (b) 7500 (c) 750
  4. 4.√27 to 1 decimal place? (a) 5.4 (b) 5.2 (c) 5.1 (d) 5.3
  5. 5.Best estimate of 1824 ÷ 76? (a) 2300 (b) 230 (c) 23
  6. 6.Best estimate of 1262 ÷ 79? (a) 1600 (b) 16 (c) 160
  7. 7.√31 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.6 (d) 5.7
  8. 8.Best estimate of 4869 ÷ 68? (a) 700 (b) 70 (c) 7000
  9. 9.Best estimate of 1942 ÷ 37? (a) 490 (b) 49 (c) 4900
  10. 10.√21 to 1 decimal place? (a) 4.7 (b) 4.8 (c) 4.5 (d) 4.6
  11. 11.Best estimate of 3552 ÷ 51? (a) 710 (b) 7100 (c) 71
  12. 12.√50 to 1 decimal place? (a) 7.1 (b) 7.3 (c) 7.4 (d) 7.2
  13. 13.Best estimate of 2083 ÷ 28? (a) 690 (b) 6900 (c) 69
  14. 14.Best estimate of 618 ÷ 27? (a) 2100 (b) 210 (c) 21
  15. 15.√58 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 7.6 (d) 7.7
  16. 16.Best estimate of 1480 ÷ 37? (a) 3700 (b) 37 (c) 370
  17. 17.Best estimate of 1997 ÷ 29? (a) 67 (b) 6700 (c) 670
  18. 18.Best estimate of 1477 ÷ 52? (a) 300 (b) 3000 (c) 30
  19. 19.Best estimate of 2719 ÷ 79? (a) 340 (b) 3400 (c) 34
  20. 20.√51 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 7.0 (d) 7.3
  21. 21.√35 to 1 decimal place? (a) 5.8 (b) 6.1 (c) 6.0 (d) 5.9
  22. 22.Best estimate of 1082 ÷ 49? (a) 22 (b) 220 (c) 2200
  23. 23.Best estimate of 2288 ÷ 67? (a) 330 (b) 3300 (c) 33
  24. 24.√62 to 1 decimal place? (a) 8.0 (b) 8.2 (c) 7.9 (d) 8.1
  25. 25.√71 to 1 decimal place? (a) 8.3 (b) 8.5 (c) 8.4 (d) 8.6
  26. 26.Best estimate of 3416 ÷ 74? (a) 49 (b) 4900 (c) 490
  27. 27.Best estimate of 2652 ÷ 66? (a) 3800 (b) 380 (c) 38
  28. 28.Best estimate of 2108 ÷ 29? (a) 700 (b) 7000 (c) 70
  29. 29.Best estimate of 2781 ÷ 83? (a) 3500 (b) 350 (c) 35
  30. 30.√69 to 1 decimal place? (a) 8.5 (b) 8.3 (c) 8.6 (d) 8.4
  31. 31.Best estimate of 2147 ÷ 73? (a) 31 (b) 3100 (c) 310
  32. 32.√82 to 1 decimal place? (a) 8.9 (b) 9.1 (c) 9.2 (d) 9.0
  33. 33.√65 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.1 (d) 8.0
  34. 34.√61 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 7.6 (d) 7.9
  35. 35.Best estimate of 2372 ÷ 61? (a) 400 (b) 40 (c) 4000
  36. 36.Best estimate of 3241 ÷ 36? (a) 810 (b) 81 (c) 8100
  37. 37.√66 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 8.3 (d) 8.2
  38. 38.√28 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.3 (d) 5.6
  39. 39.Best estimate of 5442 ÷ 59? (a) 910 (b) 9100 (c) 91
  40. 40.Best estimate of 1624 ÷ 46? (a) 320 (b) 32 (c) 3200

Answer key

  1. 5.8
  2. 9.4
  3. 75
  4. 5.2
  5. 23
  6. 16
  7. 5.6
  8. 70
  9. 49
  10. 4.6
  11. 71
  12. 7.1
  13. 69
  14. 21
  15. 7.6
  16. 37
  17. 67
  18. 30
  19. 34
  20. 7.1
  21. 5.9
  22. 22
  23. 33
  24. 7.9
  25. 8.4
  26. 49
  27. 38
  28. 70
  29. 35
  30. 8.3
  31. 31
  32. 9.1
  33. 8.1
  34. 7.8
  35. 40
  36. 81
  37. 8.1
  38. 5.3
  39. 91
  40. 32

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