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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 25 · 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.√37 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.1 (d) 6.0
  2. 2.√34 to 1 decimal place? (a) 6.0 (b) 6.1 (c) 5.8 (d) 5.9
  3. 3.Best estimate of 1177 ÷ 78? (a) 15 (b) 150 (c) 1500
  4. 4.√61 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 8.1 (d) 8.0
  5. 5.Best estimate of 432 ÷ 23? (a) 22 (b) 220 (c) 2200
  6. 6.Best estimate of 2517 ÷ 41? (a) 630 (b) 63 (c) 6300
  7. 7.Best estimate of 2015 ÷ 41? (a) 5000 (b) 50 (c) 500
  8. 8.√86 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.3 (d) 9.6
  9. 9.√85 to 1 decimal place? (a) 9.2 (b) 8.9 (c) 9.1 (d) 9.0
  10. 10.Best estimate of 988 ÷ 71? (a) 14 (b) 1400 (c) 140
  11. 11.Best estimate of 774 ÷ 22? (a) 39 (b) 3900 (c) 390
  12. 12.Best estimate of 2514 ÷ 62? (a) 42 (b) 420 (c) 4200
  13. 13.Best estimate of 434 ÷ 27? (a) 1400 (b) 140 (c) 14
  14. 14.√47 to 1 decimal place? (a) 6.7 (b) 6.9 (c) 7.0 (d) 6.8
  15. 15.√63 to 1 decimal place? (a) 7.9 (b) 8.2 (c) 8.0 (d) 8.1
  16. 16.√56 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.5 (d) 7.6
  17. 17.Best estimate of 3550 ÷ 73? (a) 510 (b) 5100 (c) 51
  18. 18.Best estimate of 2100 ÷ 72? (a) 3000 (b) 300 (c) 30
  19. 19.Best estimate of 886 ÷ 47? (a) 180 (b) 18 (c) 1800
  20. 20.Best estimate of 692 ÷ 26? (a) 230 (b) 23 (c) 2300
  21. 21.Best estimate of 1315 ÷ 23? (a) 66 (b) 660 (c) 6600
  22. 22.√69 to 1 decimal place? (a) 8.2 (b) 8.0 (c) 8.3 (d) 8.1
  23. 23.Best estimate of 1225 ÷ 36? (a) 3100 (b) 310 (c) 31
  24. 24.√32 to 1 decimal place? (a) 5.6 (b) 5.7 (c) 5.9 (d) 5.8
  25. 25.Best estimate of 994 ÷ 26? (a) 330 (b) 33 (c) 3300
  26. 26.Best estimate of 813 ÷ 33? (a) 27 (b) 2700 (c) 270
  27. 27.Best estimate of 508 ÷ 38? (a) 1300 (b) 13 (c) 130
  28. 28.Best estimate of 1478 ÷ 67? (a) 210 (b) 2100 (c) 21
  29. 29.√88 to 1 decimal place? (a) 9.3 (b) 9.6 (c) 9.5 (d) 9.4
  30. 30.√28 to 1 decimal place? (a) 5.1 (b) 5.3 (c) 5.4 (d) 5.2
  31. 31.Best estimate of 1294 ÷ 33? (a) 4300 (b) 43 (c) 430
  32. 32.√26 to 1 decimal place? (a) 5.3 (b) 5.1 (c) 5.2 (d) 5.4
  33. 33.Best estimate of 3794 ÷ 48? (a) 76 (b) 760 (c) 7600
  34. 34.Best estimate of 541 ÷ 42? (a) 1400 (b) 14 (c) 140
  35. 35.Best estimate of 2024 ÷ 33? (a) 670 (b) 67 (c) 6700
  36. 36.√50 to 1 decimal place? (a) 7.3 (b) 7.2 (c) 7.1 (d) 7.0
  37. 37.Best estimate of 4199 ÷ 64? (a) 7000 (b) 700 (c) 70
  38. 38.√96 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.8 (d) 9.9
  39. 39.Best estimate of 3501 ÷ 82? (a) 440 (b) 4400 (c) 44
  40. 40.√30 to 1 decimal place? (a) 5.5 (b) 5.8 (c) 5.6 (d) 5.7

Answer key

  1. 6.1
  2. 5.8
  3. 15
  4. 7.8
  5. 22
  6. 63
  7. 50
  8. 9.3
  9. 9.2
  10. 14
  11. 39
  12. 42
  13. 14
  14. 6.9
  15. 7.9
  16. 7.5
  17. 51
  18. 30
  19. 18
  20. 23
  21. 66
  22. 8.3
  23. 31
  24. 5.7
  25. 33
  26. 27
  27. 13
  28. 21
  29. 9.4
  30. 5.3
  31. 43
  32. 5.1
  33. 76
  34. 14
  35. 67
  36. 7.1
  37. 70
  38. 9.8
  39. 44
  40. 5.5

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