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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 766 · 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 5310 ÷ 81? (a) 660 (b) 66 (c) 6600
  2. 2.√94 to 1 decimal place? (a) 10.0 (b) 9.8 (c) 9.9 (d) 9.7
  3. 3.Best estimate of 2149 ÷ 23? (a) 1070 (b) 107 (c) 10700
  4. 4.Best estimate of 574 ÷ 22? (a) 290 (b) 2900 (c) 29
  5. 5.Best estimate of 844 ÷ 56? (a) 140 (b) 1400 (c) 14
  6. 6.√69 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.3 (d) 8.6
  7. 7.√85 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.1 (d) 9.0
  8. 8.√27 to 1 decimal place? (a) 5.5 (b) 5.3 (c) 5.2 (d) 5.4
  9. 9.Best estimate of 1329 ÷ 38? (a) 330 (b) 3300 (c) 33
  10. 10.Best estimate of 1521 ÷ 48? (a) 300 (b) 30 (c) 3000
  11. 11.Best estimate of 3256 ÷ 88? (a) 360 (b) 3600 (c) 36
  12. 12.Best estimate of 2917 ÷ 89? (a) 3200 (b) 32 (c) 320
  13. 13.Best estimate of 4123 ÷ 56? (a) 6900 (b) 690 (c) 69
  14. 14.Best estimate of 1453 ÷ 28? (a) 48 (b) 480 (c) 4800
  15. 15.Best estimate of 2045 ÷ 34? (a) 6800 (b) 680 (c) 68
  16. 16.√29 to 1 decimal place? (a) 5.2 (b) 5.4 (c) 5.3 (d) 5.1
  17. 17.Best estimate of 2353 ÷ 54? (a) 47 (b) 4700 (c) 470
  18. 18.√90 to 1 decimal place? (a) 9.6 (b) 9.5 (c) 9.4 (d) 9.3
  19. 19.Best estimate of 2668 ÷ 29? (a) 890 (b) 8900 (c) 89
  20. 20.Best estimate of 5766 ÷ 76? (a) 7200 (b) 72 (c) 720
  21. 21.Best estimate of 966 ÷ 22? (a) 48 (b) 480 (c) 4800
  22. 22.Best estimate of 1199 ÷ 74? (a) 1700 (b) 17 (c) 170
  23. 23.Best estimate of 685 ÷ 32? (a) 23 (b) 230 (c) 2300
  24. 24.√74 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.3 (d) 8.4
  25. 25.√45 to 1 decimal place? (a) 6.6 (b) 6.4 (c) 6.5 (d) 6.7
  26. 26.√56 to 1 decimal place? (a) 7.7 (b) 7.5 (c) 7.8 (d) 7.6
  27. 27.√88 to 1 decimal place? (a) 9.7 (b) 9.4 (c) 9.6 (d) 9.5
  28. 28.√53 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.3 (d) 7.6
  29. 29.√23 to 1 decimal place? (a) 5.1 (b) 4.9 (c) 5.0 (d) 4.8
  30. 30.Best estimate of 6944 ÷ 73? (a) 990 (b) 99 (c) 9900
  31. 31.Best estimate of 1278 ÷ 58? (a) 2100 (b) 21 (c) 210
  32. 32.Best estimate of 1719 ÷ 27? (a) 570 (b) 5700 (c) 57
  33. 33.Best estimate of 4054 ÷ 44? (a) 1010 (b) 101 (c) 10100
  34. 34.Best estimate of 2722 ÷ 62? (a) 450 (b) 4500 (c) 45
  35. 35.√82 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 8.9 (d) 8.8
  36. 36.√66 to 1 decimal place? (a) 8.4 (b) 8.2 (c) 8.3 (d) 8.1
  37. 37.Best estimate of 430 ÷ 24? (a) 2200 (b) 220 (c) 22
  38. 38.√20 to 1 decimal place? (a) 4.5 (b) 4.4 (c) 4.7 (d) 4.6
  39. 39.Best estimate of 864 ÷ 37? (a) 2200 (b) 22 (c) 220
  40. 40.√40 to 1 decimal place? (a) 6.5 (b) 6.2 (c) 6.3 (d) 6.4

Answer key

  1. 66
  2. 9.7
  3. 107
  4. 29
  5. 14
  6. 8.3
  7. 9.2
  8. 5.2
  9. 33
  10. 30
  11. 36
  12. 32
  13. 69
  14. 48
  15. 68
  16. 5.4
  17. 47
  18. 9.5
  19. 89
  20. 72
  21. 48
  22. 17
  23. 23
  24. 8.6
  25. 6.7
  26. 7.5
  27. 9.4
  28. 7.3
  29. 4.8
  30. 99
  31. 21
  32. 57
  33. 101
  34. 45
  35. 9.1
  36. 8.1
  37. 22
  38. 4.5
  39. 22
  40. 6.3

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