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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 305 · 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.√78 to 1 decimal place? (a) 8.9 (b) 8.7 (c) 8.8 (d) 8.6
  2. 2.Best estimate of 1150 ÷ 36? (a) 2900 (b) 29 (c) 290
  3. 3.√65 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.3 (d) 8.4
  4. 4.Best estimate of 2253 ÷ 29? (a) 75 (b) 7500 (c) 750
  5. 5.Best estimate of 798 ÷ 46? (a) 1600 (b) 160 (c) 16
  6. 6.√59 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.7 (d) 7.8
  7. 7.√62 to 1 decimal place? (a) 7.6 (b) 7.9 (c) 7.7 (d) 7.8
  8. 8.√31 to 1 decimal place? (a) 5.7 (b) 5.8 (c) 5.9 (d) 5.6
  9. 9.Best estimate of 666 ÷ 32? (a) 220 (b) 22 (c) 2200
  10. 10.Best estimate of 2944 ÷ 32? (a) 9800 (b) 980 (c) 98
  11. 11.√79 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 8.9 (d) 8.8
  12. 12.√87 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.4 (d) 9.3
  13. 13.Best estimate of 2422 ÷ 34? (a) 8100 (b) 81 (c) 810
  14. 14.Best estimate of 4352 ÷ 51? (a) 87 (b) 870 (c) 8700
  15. 15.√85 to 1 decimal place? (a) 9.0 (b) 9.2 (c) 8.9 (d) 9.1
  16. 16.Best estimate of 1591 ÷ 52? (a) 3200 (b) 320 (c) 32
  17. 17.√83 to 1 decimal place? (a) 8.9 (b) 9.1 (c) 9.0 (d) 9.2
  18. 18.Best estimate of 3623 ÷ 41? (a) 9100 (b) 910 (c) 91
  19. 19.√56 to 1 decimal place? (a) 7.6 (b) 7.7 (c) 7.5 (d) 7.8
  20. 20.Best estimate of 5822 ÷ 61? (a) 9700 (b) 970 (c) 97
  21. 21.Best estimate of 1149 ÷ 51? (a) 230 (b) 2300 (c) 23
  22. 22.Best estimate of 608 ÷ 34? (a) 2000 (b) 200 (c) 20
  23. 23.Best estimate of 3467 ÷ 38? (a) 87 (b) 870 (c) 8700
  24. 24.Best estimate of 3000 ÷ 56? (a) 500 (b) 5000 (c) 50
  25. 25.√71 to 1 decimal place? (a) 8.6 (b) 8.4 (c) 8.5 (d) 8.7
  26. 26.Best estimate of 378 ÷ 29? (a) 130 (b) 13 (c) 1300
  27. 27.√98 to 1 decimal place? (a) 9.8 (b) 10.0 (c) 10.1 (d) 9.9
  28. 28.Best estimate of 2100 ÷ 26? (a) 700 (b) 7000 (c) 70
  29. 29.Best estimate of 760 ÷ 32? (a) 250 (b) 25 (c) 2500
  30. 30.Best estimate of 1929 ÷ 33? (a) 6400 (b) 64 (c) 640
  31. 31.Best estimate of 2819 ÷ 86? (a) 310 (b) 31 (c) 3100
  32. 32.Best estimate of 1399 ÷ 52? (a) 2800 (b) 28 (c) 280
  33. 33.Best estimate of 5115 ÷ 58? (a) 85 (b) 8500 (c) 850
  34. 34.Best estimate of 1524 ÷ 63? (a) 25 (b) 250 (c) 2500
  35. 35.Best estimate of 4040 ÷ 68? (a) 5800 (b) 58 (c) 580
  36. 36.√55 to 1 decimal place? (a) 7.5 (b) 7.3 (c) 7.2 (d) 7.4
  37. 37.√40 to 1 decimal place? (a) 6.5 (b) 6.4 (c) 6.3 (d) 6.2
  38. 38.Best estimate of 5998 ÷ 63? (a) 10000 (b) 100 (c) 1000
  39. 39.√41 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.2 (d) 6.3
  40. 40.√82 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.1 (d) 9.4

Answer key

  1. 8.8
  2. 29
  3. 8.1
  4. 75
  5. 16
  6. 7.7
  7. 7.9
  8. 5.6
  9. 22
  10. 98
  11. 8.9
  12. 9.3
  13. 81
  14. 87
  15. 9.2
  16. 32
  17. 9.1
  18. 91
  19. 7.5
  20. 97
  21. 23
  22. 20
  23. 87
  24. 50
  25. 8.4
  26. 13
  27. 9.9
  28. 70
  29. 25
  30. 64
  31. 31
  32. 28
  33. 85
  34. 25
  35. 58
  36. 7.4
  37. 6.3
  38. 100
  39. 6.4
  40. 9.1

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