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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 227 · 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 7258 ÷ 83? (a) 9100 (b) 91 (c) 910
  2. 2.√85 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.3 (d) 9.2
  3. 3.√59 to 1 decimal place? (a) 7.9 (b) 7.7 (c) 8.0 (d) 7.8
  4. 4.Best estimate of 6860 ÷ 89? (a) 760 (b) 7600 (c) 76
  5. 5.√61 to 1 decimal place? (a) 7.7 (b) 7.9 (c) 7.8 (d) 8.0
  6. 6.√98 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 9.9 (d) 9.6
  7. 7.Best estimate of 2979 ÷ 56? (a) 50 (b) 5000 (c) 500
  8. 8.√30 to 1 decimal place? (a) 5.7 (b) 5.8 (c) 5.5 (d) 5.6
  9. 9.√94 to 1 decimal place? (a) 9.7 (b) 9.4 (c) 9.5 (d) 9.6
  10. 10.Best estimate of 6308 ÷ 72? (a) 90 (b) 900 (c) 9000
  11. 11.√65 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 7.9 (d) 8.0
  12. 12.Best estimate of 1980 ÷ 34? (a) 660 (b) 6600 (c) 66
  13. 13.√34 to 1 decimal place? (a) 5.7 (b) 5.8 (c) 5.9 (d) 5.6
  14. 14.√77 to 1 decimal place? (a) 9.1 (b) 8.8 (c) 8.9 (d) 9.0
  15. 15.Best estimate of 3239 ÷ 68? (a) 460 (b) 46 (c) 4600
  16. 16.Best estimate of 1571 ÷ 86? (a) 1700 (b) 17 (c) 170
  17. 17.√87 to 1 decimal place? (a) 9.4 (b) 9.2 (c) 9.5 (d) 9.3
  18. 18.√88 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.5 (d) 9.6
  19. 19.√83 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 9.0 (d) 9.1
  20. 20.√75 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.4 (d) 8.5
  21. 21.Best estimate of 983 ÷ 26? (a) 3300 (b) 330 (c) 33
  22. 22.Best estimate of 2682 ÷ 31? (a) 8900 (b) 890 (c) 89
  23. 23.Best estimate of 1614 ÷ 23? (a) 810 (b) 81 (c) 8100
  24. 24.Best estimate of 6231 ÷ 86? (a) 690 (b) 6900 (c) 69
  25. 25.Best estimate of 1781 ÷ 67? (a) 250 (b) 2500 (c) 25
  26. 26.√67 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.4 (d) 8.1
  27. 27.Best estimate of 4691 ÷ 84? (a) 59 (b) 590 (c) 5900
  28. 28.Best estimate of 6035 ÷ 71? (a) 8600 (b) 860 (c) 86
  29. 29.Best estimate of 4063 ÷ 62? (a) 680 (b) 6800 (c) 68
  30. 30.Best estimate of 2175 ÷ 31? (a) 73 (b) 730 (c) 7300
  31. 31.√22 to 1 decimal place? (a) 4.6 (b) 4.9 (c) 4.7 (d) 4.8
  32. 32.Best estimate of 1340 ÷ 24? (a) 6700 (b) 670 (c) 67
  33. 33.√21 to 1 decimal place? (a) 4.7 (b) 4.5 (c) 4.6 (d) 4.8
  34. 34.Best estimate of 1852 ÷ 34? (a) 6200 (b) 620 (c) 62
  35. 35.√72 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.6 (d) 8.3
  36. 36.Best estimate of 1614 ÷ 68? (a) 2300 (b) 230 (c) 23
  37. 37.√76 to 1 decimal place? (a) 8.8 (b) 8.7 (c) 8.9 (d) 9.0
  38. 38.Best estimate of 5436 ÷ 76? (a) 68 (b) 6800 (c) 680
  39. 39.Best estimate of 3325 ÷ 63? (a) 55 (b) 550 (c) 5500
  40. 40.√43 to 1 decimal place? (a) 6.4 (b) 6.6 (c) 6.3 (d) 6.5

Answer key

  1. 91
  2. 9.2
  3. 7.7
  4. 76
  5. 7.8
  6. 9.9
  7. 50
  8. 5.5
  9. 9.7
  10. 90
  11. 8.1
  12. 66
  13. 5.8
  14. 8.8
  15. 46
  16. 17
  17. 9.3
  18. 9.4
  19. 9.1
  20. 8.7
  21. 33
  22. 89
  23. 81
  24. 69
  25. 25
  26. 8.2
  27. 59
  28. 86
  29. 68
  30. 73
  31. 4.7
  32. 67
  33. 4.6
  34. 62
  35. 8.5
  36. 23
  37. 8.7
  38. 68
  39. 55
  40. 6.6

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