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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 171 · 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 1372 ÷ 28? (a) 4600 (b) 46 (c) 460
  2. 2.Best estimate of 1848 ÷ 56? (a) 310 (b) 3100 (c) 31
  3. 3.√26 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.1 (d) 5.2
  4. 4.√59 to 1 decimal place? (a) 8.0 (b) 7.8 (c) 7.9 (d) 7.7
  5. 5.√71 to 1 decimal place? (a) 8.4 (b) 8.2 (c) 8.3 (d) 8.5
  6. 6.√22 to 1 decimal place? (a) 4.8 (b) 4.7 (c) 4.6 (d) 4.5
  7. 7.Best estimate of 1788 ÷ 38? (a) 450 (b) 4500 (c) 45
  8. 8.Best estimate of 3568 ÷ 69? (a) 5100 (b) 510 (c) 51
  9. 9.√37 to 1 decimal place? (a) 6.4 (b) 6.2 (c) 6.1 (d) 6.3
  10. 10.√82 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.1 (d) 9.4
  11. 11.Best estimate of 2043 ÷ 36? (a) 5100 (b) 510 (c) 51
  12. 12.√74 to 1 decimal place? (a) 8.7 (b) 8.5 (c) 8.6 (d) 8.4
  13. 13.√80 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 8.7 (d) 8.8
  14. 14.√72 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.3 (d) 8.6
  15. 15.√75 to 1 decimal place? (a) 8.6 (b) 8.4 (c) 8.5 (d) 8.7
  16. 16.Best estimate of 510 ÷ 34? (a) 17 (b) 1700 (c) 170
  17. 17.Best estimate of 1811 ÷ 62? (a) 30 (b) 300 (c) 3000
  18. 18.√41 to 1 decimal place? (a) 6.4 (b) 6.6 (c) 6.5 (d) 6.3
  19. 19.√55 to 1 decimal place? (a) 7.5 (b) 7.2 (c) 7.4 (d) 7.3
  20. 20.Best estimate of 1492 ÷ 52? (a) 300 (b) 3000 (c) 30
  21. 21.√92 to 1 decimal place? (a) 9.7 (b) 9.5 (c) 9.6 (d) 9.8
  22. 22.Best estimate of 2450 ÷ 76? (a) 3100 (b) 31 (c) 310
  23. 23.Best estimate of 4260 ÷ 47? (a) 8500 (b) 850 (c) 85
  24. 24.√42 to 1 decimal place? (a) 6.6 (b) 6.8 (c) 6.7 (d) 6.5
  25. 25.√40 to 1 decimal place? (a) 6.6 (b) 6.4 (c) 6.5 (d) 6.3
  26. 26.Best estimate of 3321 ÷ 47? (a) 6600 (b) 66 (c) 660
  27. 27.√58 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 7.5 (d) 7.6
  28. 28.Best estimate of 2713 ÷ 46? (a) 5400 (b) 54 (c) 540
  29. 29.Best estimate of 1989 ÷ 34? (a) 660 (b) 6600 (c) 66
  30. 30.√96 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.8 (d) 9.5
  31. 31.Best estimate of 3403 ÷ 89? (a) 3800 (b) 380 (c) 38
  32. 32.Best estimate of 1031 ÷ 82? (a) 130 (b) 13 (c) 1300
  33. 33.Best estimate of 2947 ÷ 66? (a) 42 (b) 4200 (c) 420
  34. 34.Best estimate of 1425 ÷ 64? (a) 2400 (b) 240 (c) 24
  35. 35.Best estimate of 1676 ÷ 32? (a) 560 (b) 5600 (c) 56
  36. 36.√21 to 1 decimal place? (a) 4.7 (b) 4.6 (c) 4.8 (d) 4.5
  37. 37.√48 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.8 (d) 6.9
  38. 38.Best estimate of 3343 ÷ 43? (a) 84 (b) 840 (c) 8400
  39. 39.Best estimate of 3413 ÷ 61? (a) 5700 (b) 57 (c) 570
  40. 40.√23 to 1 decimal place? (a) 4.7 (b) 4.6 (c) 4.5 (d) 4.8

Answer key

  1. 46
  2. 31
  3. 5.1
  4. 7.7
  5. 8.4
  6. 4.7
  7. 45
  8. 51
  9. 6.1
  10. 9.1
  11. 51
  12. 8.6
  13. 8.9
  14. 8.5
  15. 8.7
  16. 17
  17. 30
  18. 6.4
  19. 7.4
  20. 30
  21. 9.6
  22. 31
  23. 85
  24. 6.5
  25. 6.3
  26. 66
  27. 7.6
  28. 54
  29. 66
  30. 9.8
  31. 38
  32. 13
  33. 42
  34. 24
  35. 56
  36. 4.6
  37. 6.9
  38. 84
  39. 57
  40. 4.8

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