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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 352 · 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 1767 ÷ 27? (a) 590 (b) 5900 (c) 59
  2. 2.Best estimate of 2708 ÷ 74? (a) 390 (b) 3900 (c) 39
  3. 3.Best estimate of 2204 ÷ 64? (a) 37 (b) 370 (c) 3700
  4. 4.√41 to 1 decimal place? (a) 6.5 (b) 6.7 (c) 6.6 (d) 6.4
  5. 5.Best estimate of 1435 ÷ 22? (a) 7200 (b) 720 (c) 72
  6. 6.√89 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.2 (d) 9.1
  7. 7.√69 to 1 decimal place? (a) 8.3 (b) 8.5 (c) 8.4 (d) 8.6
  8. 8.Best estimate of 315 ÷ 26? (a) 11 (b) 110 (c) 1100
  9. 9.√24 to 1 decimal place? (a) 4.8 (b) 5.1 (c) 5.0 (d) 4.9
  10. 10.√27 to 1 decimal place? (a) 5.2 (b) 5.1 (c) 5.3 (d) 5.0
  11. 11.√30 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.5 (d) 5.2
  12. 12.Best estimate of 3983 ÷ 54? (a) 80 (b) 8000 (c) 800
  13. 13.√92 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 9.6 (d) 9.8
  14. 14.Best estimate of 1317 ÷ 23? (a) 66 (b) 6600 (c) 660
  15. 15.Best estimate of 3497 ÷ 48? (a) 70 (b) 700 (c) 7000
  16. 16.Best estimate of 2146 ÷ 82? (a) 2700 (b) 270 (c) 27
  17. 17.Best estimate of 1051 ÷ 37? (a) 26 (b) 260 (c) 2600
  18. 18.√61 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 7.9 (d) 8.0
  19. 19.√47 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 6.8 (d) 6.7
  20. 20.Best estimate of 4662 ÷ 51? (a) 9300 (b) 93 (c) 930
  21. 21.√75 to 1 decimal place? (a) 8.8 (b) 9.0 (c) 8.7 (d) 8.9
  22. 22.√66 to 1 decimal place? (a) 8.3 (b) 8.1 (c) 8.4 (d) 8.2
  23. 23.√56 to 1 decimal place? (a) 7.5 (b) 7.7 (c) 7.6 (d) 7.4
  24. 24.Best estimate of 6177 ÷ 72? (a) 8800 (b) 88 (c) 880
  25. 25.√58 to 1 decimal place? (a) 7.4 (b) 7.6 (c) 7.3 (d) 7.5
  26. 26.√55 to 1 decimal place? (a) 7.3 (b) 7.2 (c) 7.1 (d) 7.4
  27. 27.√26 to 1 decimal place? (a) 5.0 (b) 5.3 (c) 5.2 (d) 5.1
  28. 28.√38 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.3 (d) 6.1
  29. 29.√32 to 1 decimal place? (a) 5.6 (b) 5.9 (c) 5.7 (d) 5.8
  30. 30.Best estimate of 1257 ÷ 52? (a) 25 (b) 250 (c) 2500
  31. 31.Best estimate of 2061 ÷ 43? (a) 5200 (b) 520 (c) 52
  32. 32.Best estimate of 2449 ÷ 77? (a) 3100 (b) 31 (c) 310
  33. 33.Best estimate of 914 ÷ 57? (a) 1500 (b) 150 (c) 15
  34. 34.Best estimate of 1040 ÷ 29? (a) 350 (b) 35 (c) 3500
  35. 35.Best estimate of 3850 ÷ 82? (a) 4800 (b) 48 (c) 480
  36. 36.Best estimate of 3104 ÷ 36? (a) 78 (b) 780 (c) 7800
  37. 37.√82 to 1 decimal place? (a) 9.2 (b) 8.9 (c) 9.1 (d) 9.0
  38. 38.√50 to 1 decimal place? (a) 7.2 (b) 7.3 (c) 7.1 (d) 7.0
  39. 39.Best estimate of 4466 ÷ 78? (a) 560 (b) 5600 (c) 56
  40. 40.Best estimate of 3668 ÷ 69? (a) 52 (b) 520 (c) 5200

Answer key

  1. 59
  2. 39
  3. 37
  4. 6.4
  5. 72
  6. 9.4
  7. 8.3
  8. 11
  9. 4.9
  10. 5.2
  11. 5.5
  12. 80
  13. 9.6
  14. 66
  15. 70
  16. 27
  17. 26
  18. 7.8
  19. 6.9
  20. 93
  21. 8.7
  22. 8.1
  23. 7.5
  24. 88
  25. 7.6
  26. 7.4
  27. 5.1
  28. 6.2
  29. 5.7
  30. 25
  31. 52
  32. 31
  33. 15
  34. 35
  35. 48
  36. 78
  37. 9.1
  38. 7.1
  39. 56
  40. 52

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