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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 405 · 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 2114 ÷ 26? (a) 7000 (b) 700 (c) 70
  2. 2.√40 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.3 (d) 6.6
  3. 3.Best estimate of 5543 ÷ 89? (a) 6200 (b) 62 (c) 620
  4. 4.Best estimate of 2280 ÷ 63? (a) 380 (b) 3800 (c) 38
  5. 5.√45 to 1 decimal place? (a) 7.0 (b) 6.9 (c) 6.8 (d) 6.7
  6. 6.√98 to 1 decimal place? (a) 10.0 (b) 9.9 (c) 10.2 (d) 10.1
  7. 7.√29 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.5 (d) 5.6
  8. 8.Best estimate of 4037 ÷ 53? (a) 8100 (b) 810 (c) 81
  9. 9.√61 to 1 decimal place? (a) 8.0 (b) 7.7 (c) 7.9 (d) 7.8
  10. 10.√92 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.3 (d) 9.6
  11. 11.√82 to 1 decimal place? (a) 9.0 (b) 8.8 (c) 8.9 (d) 9.1
  12. 12.Best estimate of 1297 ÷ 36? (a) 32 (b) 3200 (c) 320
  13. 13.Best estimate of 3014 ÷ 32? (a) 10000 (b) 100 (c) 1000
  14. 14.√31 to 1 decimal place? (a) 5.5 (b) 5.6 (c) 5.4 (d) 5.7
  15. 15.√41 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.2 (d) 6.1
  16. 16.√51 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 6.8 (d) 7.1
  17. 17.Best estimate of 3341 ÷ 72? (a) 4800 (b) 48 (c) 480
  18. 18.Best estimate of 796 ÷ 36? (a) 20 (b) 200 (c) 2000
  19. 19.√22 to 1 decimal place? (a) 4.4 (b) 4.7 (c) 4.5 (d) 4.6
  20. 20.Best estimate of 6047 ÷ 88? (a) 670 (b) 67 (c) 6700
  21. 21.Best estimate of 2360 ÷ 68? (a) 340 (b) 34 (c) 3400
  22. 22.Best estimate of 4006 ÷ 42? (a) 1000 (b) 10000 (c) 100
  23. 23.√79 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.6 (d) 8.7
  24. 24.Best estimate of 1365 ÷ 78? (a) 17 (b) 1700 (c) 170
  25. 25.√50 to 1 decimal place? (a) 7.1 (b) 6.8 (c) 6.9 (d) 7.0
  26. 26.Best estimate of 1912 ÷ 36? (a) 480 (b) 4800 (c) 48
  27. 27.√69 to 1 decimal place? (a) 8.4 (b) 8.1 (c) 8.3 (d) 8.2
  28. 28.√71 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.7 (d) 8.6
  29. 29.√24 to 1 decimal place? (a) 4.9 (b) 4.8 (c) 4.6 (d) 4.7
  30. 30.Best estimate of 4153 ÷ 47? (a) 83 (b) 8300 (c) 830
  31. 31.Best estimate of 4800 ÷ 79? (a) 6000 (b) 600 (c) 60
  32. 32.√55 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.1 (d) 7.2
  33. 33.√56 to 1 decimal place? (a) 7.5 (b) 7.3 (c) 7.4 (d) 7.6
  34. 34.Best estimate of 3222 ÷ 69? (a) 460 (b) 46 (c) 4600
  35. 35.√32 to 1 decimal place? (a) 5.6 (b) 5.4 (c) 5.5 (d) 5.7
  36. 36.Best estimate of 2509 ÷ 36? (a) 6300 (b) 630 (c) 63
  37. 37.√26 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 4.8 (d) 4.9
  38. 38.Best estimate of 2422 ÷ 48? (a) 48 (b) 480 (c) 4800
  39. 39.√20 to 1 decimal place? (a) 4.8 (b) 4.5 (c) 4.7 (d) 4.6
  40. 40.Best estimate of 4781 ÷ 54? (a) 9600 (b) 96 (c) 960

Answer key

  1. 70
  2. 6.3
  3. 62
  4. 38
  5. 6.7
  6. 9.9
  7. 5.4
  8. 81
  9. 7.8
  10. 9.6
  11. 9.1
  12. 32
  13. 100
  14. 5.6
  15. 6.4
  16. 7.1
  17. 48
  18. 20
  19. 4.7
  20. 67
  21. 34
  22. 100
  23. 8.9
  24. 17
  25. 7.1
  26. 48
  27. 8.3
  28. 8.4
  29. 4.9
  30. 83
  31. 60
  32. 7.4
  33. 7.5
  34. 46
  35. 5.7
  36. 63
  37. 5.1
  38. 48
  39. 4.5
  40. 96

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