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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 306 · 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 4854 ÷ 56? (a) 81 (b) 810 (c) 8100
  2. 2.Best estimate of 582 ÷ 46? (a) 12 (b) 1200 (c) 120
  3. 3.√34 to 1 decimal place? (a) 5.7 (b) 5.9 (c) 5.8 (d) 5.6
  4. 4.Best estimate of 6677 ÷ 71? (a) 950 (b) 9500 (c) 95
  5. 5.√85 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.1 (d) 9.0
  6. 6.√98 to 1 decimal place? (a) 10.2 (b) 10.1 (c) 10.0 (d) 9.9
  7. 7.√76 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.6 (d) 8.9
  8. 8.Best estimate of 2578 ÷ 66? (a) 370 (b) 3700 (c) 37
  9. 9.Best estimate of 1797 ÷ 36? (a) 45 (b) 450 (c) 4500
  10. 10.√55 to 1 decimal place? (a) 7.3 (b) 7.4 (c) 7.5 (d) 7.2
  11. 11.Best estimate of 4928 ÷ 52? (a) 99 (b) 9900 (c) 990
  12. 12.Best estimate of 729 ÷ 52? (a) 15 (b) 1500 (c) 150
  13. 13.Best estimate of 775 ÷ 28? (a) 26 (b) 260 (c) 2600
  14. 14.Best estimate of 5334 ÷ 68? (a) 760 (b) 7600 (c) 76
  15. 15.Best estimate of 617 ÷ 51? (a) 1200 (b) 120 (c) 12
  16. 16.√88 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.2 (d) 9.5
  17. 17.√83 to 1 decimal place? (a) 9.2 (b) 8.9 (c) 9.1 (d) 9.0
  18. 18.√48 to 1 decimal place? (a) 6.9 (b) 7.2 (c) 7.0 (d) 7.1
  19. 19.Best estimate of 1899 ÷ 59? (a) 3200 (b) 320 (c) 32
  20. 20.Best estimate of 7666 ÷ 86? (a) 8500 (b) 85 (c) 850
  21. 21.√43 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.5 (d) 6.4
  22. 22.Best estimate of 4087 ÷ 62? (a) 680 (b) 6800 (c) 68
  23. 23.√58 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 7.9 (d) 7.6
  24. 24.√66 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.2 (d) 8.1
  25. 25.Best estimate of 2142 ÷ 26? (a) 71 (b) 7100 (c) 710
  26. 26.Best estimate of 5516 ÷ 63? (a) 9200 (b) 920 (c) 92
  27. 27.√28 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.3 (d) 5.2
  28. 28.Best estimate of 849 ÷ 22? (a) 42 (b) 4200 (c) 420
  29. 29.√51 to 1 decimal place? (a) 7.0 (b) 7.2 (c) 7.1 (d) 6.9
  30. 30.Best estimate of 2351 ÷ 37? (a) 590 (b) 5900 (c) 59
  31. 31.√96 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.8 (d) 9.7
  32. 32.√47 to 1 decimal place? (a) 6.8 (b) 6.6 (c) 6.9 (d) 6.7
  33. 33.Best estimate of 1005 ÷ 52? (a) 200 (b) 20 (c) 2000
  34. 34.Best estimate of 1465 ÷ 62? (a) 24 (b) 240 (c) 2400
  35. 35.√56 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.8 (d) 7.7
  36. 36.√62 to 1 decimal place? (a) 8.1 (b) 7.9 (c) 7.8 (d) 8.0
  37. 37.Best estimate of 1076 ÷ 79? (a) 1300 (b) 130 (c) 13
  38. 38.Best estimate of 1220 ÷ 39? (a) 310 (b) 3100 (c) 31
  39. 39.√31 to 1 decimal place? (a) 5.6 (b) 5.7 (c) 5.5 (d) 5.4
  40. 40.√94 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.5 (d) 9.4

Answer key

  1. 81
  2. 12
  3. 5.8
  4. 95
  5. 9.2
  6. 9.9
  7. 8.7
  8. 37
  9. 45
  10. 7.4
  11. 99
  12. 15
  13. 26
  14. 76
  15. 12
  16. 9.4
  17. 9.1
  18. 6.9
  19. 32
  20. 85
  21. 6.6
  22. 68
  23. 7.6
  24. 8.1
  25. 71
  26. 92
  27. 5.3
  28. 42
  29. 7.1
  30. 59
  31. 9.8
  32. 6.9
  33. 20
  34. 24
  35. 7.5
  36. 7.9
  37. 13
  38. 31
  39. 5.6
  40. 9.7

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