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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 446 · 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 1236 ÷ 52? (a) 25 (b) 250 (c) 2500
  2. 2.Best estimate of 2244 ÷ 62? (a) 37 (b) 370 (c) 3700
  3. 3.√20 to 1 decimal place? (a) 4.7 (b) 4.4 (c) 4.6 (d) 4.5
  4. 4.√27 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.2 (d) 5.3
  5. 5.√55 to 1 decimal place? (a) 7.2 (b) 7.5 (c) 7.3 (d) 7.4
  6. 6.√32 to 1 decimal place? (a) 5.7 (b) 5.9 (c) 5.8 (d) 6.0
  7. 7.√37 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.1 (d) 6.0
  8. 8.Best estimate of 4006 ÷ 76? (a) 500 (b) 5000 (c) 50
  9. 9.Best estimate of 4231 ÷ 59? (a) 710 (b) 7100 (c) 71
  10. 10.Best estimate of 1411 ÷ 59? (a) 240 (b) 24 (c) 2400
  11. 11.√80 to 1 decimal place? (a) 9.0 (b) 8.8 (c) 8.9 (d) 9.1
  12. 12.Best estimate of 1402 ÷ 22? (a) 700 (b) 7000 (c) 70
  13. 13.√88 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.4 (d) 9.7
  14. 14.Best estimate of 2539 ÷ 42? (a) 6300 (b) 630 (c) 63
  15. 15.√94 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 9.9 (d) 10.0
  16. 16.√82 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.1 (d) 9.4
  17. 17.√59 to 1 decimal place? (a) 7.8 (b) 7.6 (c) 7.9 (d) 7.7
  18. 18.Best estimate of 1250 ÷ 42? (a) 310 (b) 31 (c) 3100
  19. 19.Best estimate of 989 ÷ 66? (a) 140 (b) 14 (c) 1400
  20. 20.√22 to 1 decimal place? (a) 4.7 (b) 4.8 (c) 4.9 (d) 4.6
  21. 21.√78 to 1 decimal place? (a) 9.1 (b) 8.8 (c) 9.0 (d) 8.9
  22. 22.√92 to 1 decimal place? (a) 9.8 (b) 9.5 (c) 9.6 (d) 9.7
  23. 23.√74 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.7 (d) 8.6
  24. 24.√77 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.5 (d) 8.8
  25. 25.√34 to 1 decimal place? (a) 5.6 (b) 5.9 (c) 5.8 (d) 5.7
  26. 26.Best estimate of 1033 ÷ 24? (a) 520 (b) 52 (c) 5200
  27. 27.√56 to 1 decimal place? (a) 7.3 (b) 7.6 (c) 7.4 (d) 7.5
  28. 28.Best estimate of 982 ÷ 32? (a) 33 (b) 330 (c) 3300
  29. 29.Best estimate of 479 ÷ 24? (a) 24 (b) 240 (c) 2400
  30. 30.√29 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.2 (d) 5.1
  31. 31.√50 to 1 decimal place? (a) 7.3 (b) 7.4 (c) 7.1 (d) 7.2
  32. 32.Best estimate of 7812 ÷ 82? (a) 980 (b) 98 (c) 9800
  33. 33.Best estimate of 1186 ÷ 79? (a) 150 (b) 15 (c) 1500
  34. 34.Best estimate of 4491 ÷ 56? (a) 750 (b) 75 (c) 7500
  35. 35.√96 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 10.0 (d) 9.7
  36. 36.Best estimate of 1621 ÷ 74? (a) 2300 (b) 230 (c) 23
  37. 37.Best estimate of 3818 ÷ 46? (a) 760 (b) 7600 (c) 76
  38. 38.Best estimate of 1533 ÷ 29? (a) 5100 (b) 510 (c) 51
  39. 39.Best estimate of 4138 ÷ 44? (a) 1030 (b) 103 (c) 10300
  40. 40.√62 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 8.0 (d) 8.1

Answer key

  1. 25
  2. 37
  3. 4.5
  4. 5.2
  5. 7.4
  6. 5.7
  7. 6.1
  8. 50
  9. 71
  10. 24
  11. 8.9
  12. 70
  13. 9.4
  14. 63
  15. 9.7
  16. 9.1
  17. 7.7
  18. 31
  19. 14
  20. 4.7
  21. 8.8
  22. 9.6
  23. 8.6
  24. 8.8
  25. 5.8
  26. 52
  27. 7.5
  28. 33
  29. 24
  30. 5.4
  31. 7.1
  32. 98
  33. 15
  34. 75
  35. 9.8
  36. 23
  37. 76
  38. 51
  39. 103
  40. 7.9

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