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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 928 · 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.√70 to 1 decimal place? (a) 8.6 (b) 8.4 (c) 8.7 (d) 8.5
  2. 2.√52 to 1 decimal place? (a) 7.0 (b) 7.2 (c) 6.9 (d) 7.1
  3. 3.√20 to 1 decimal place? (a) 4.8 (b) 4.6 (c) 4.7 (d) 4.5
  4. 4.Best estimate of 3551 ÷ 61? (a) 590 (b) 5900 (c) 59
  5. 5.Best estimate of 4201 ÷ 71? (a) 600 (b) 6000 (c) 60
  6. 6.Best estimate of 2429 ÷ 52? (a) 4900 (b) 49 (c) 490
  7. 7.Best estimate of 2560 ÷ 48? (a) 510 (b) 5100 (c) 51
  8. 8.Best estimate of 2996 ÷ 32? (a) 10000 (b) 1000 (c) 100
  9. 9.Best estimate of 2994 ÷ 84? (a) 3700 (b) 37 (c) 370
  10. 10.√58 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 7.6 (d) 7.9
  11. 11.√87 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.4 (d) 9.3
  12. 12.√23 to 1 decimal place? (a) 4.7 (b) 4.9 (c) 5.0 (d) 4.8
  13. 13.√46 to 1 decimal place? (a) 6.8 (b) 6.7 (c) 6.6 (d) 6.9
  14. 14.√44 to 1 decimal place? (a) 6.3 (b) 6.5 (c) 6.6 (d) 6.4
  15. 15.Best estimate of 3314 ÷ 64? (a) 5500 (b) 550 (c) 55
  16. 16.Best estimate of 5161 ÷ 86? (a) 5700 (b) 570 (c) 57
  17. 17.√61 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 8.1 (d) 8.0
  18. 18.Best estimate of 2713 ÷ 33? (a) 90 (b) 900 (c) 9000
  19. 19.Best estimate of 1458 ÷ 58? (a) 2400 (b) 24 (c) 240
  20. 20.√98 to 1 decimal place? (a) 9.8 (b) 10.0 (c) 9.7 (d) 9.9
  21. 21.√77 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 9.0 (d) 9.1
  22. 22.Best estimate of 2793 ÷ 62? (a) 47 (b) 470 (c) 4700
  23. 23.Best estimate of 4574 ÷ 59? (a) 76 (b) 760 (c) 7600
  24. 24.Best estimate of 7918 ÷ 86? (a) 880 (b) 8800 (c) 88
  25. 25.√75 to 1 decimal place? (a) 8.4 (b) 8.6 (c) 8.7 (d) 8.5
  26. 26.Best estimate of 2117 ÷ 32? (a) 710 (b) 71 (c) 7100
  27. 27.Best estimate of 2818 ÷ 89? (a) 310 (b) 3100 (c) 31
  28. 28.√62 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 7.7 (d) 7.6
  29. 29.√86 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.2 (d) 9.3
  30. 30.√85 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.5 (d) 9.2
  31. 31.Best estimate of 1226 ÷ 68? (a) 1800 (b) 18 (c) 180
  32. 32.Best estimate of 4901 ÷ 83? (a) 6100 (b) 610 (c) 61
  33. 33.Best estimate of 1706 ÷ 86? (a) 190 (b) 19 (c) 1900
  34. 34.Best estimate of 1294 ÷ 72? (a) 180 (b) 1800 (c) 18
  35. 35.Best estimate of 765 ÷ 42? (a) 1900 (b) 19 (c) 190
  36. 36.Best estimate of 4782 ÷ 57? (a) 8000 (b) 80 (c) 800
  37. 37.Best estimate of 758 ÷ 22? (a) 38 (b) 3800 (c) 380
  38. 38.√40 to 1 decimal place? (a) 6.1 (b) 6.3 (c) 6.0 (d) 6.2
  39. 39.Best estimate of 4627 ÷ 51? (a) 930 (b) 93 (c) 9300
  40. 40.Best estimate of 1710 ÷ 22? (a) 860 (b) 86 (c) 8600

Answer key

  1. 8.4
  2. 7.2
  3. 4.5
  4. 59
  5. 60
  6. 49
  7. 51
  8. 100
  9. 37
  10. 7.6
  11. 9.3
  12. 4.8
  13. 6.8
  14. 6.6
  15. 55
  16. 57
  17. 7.8
  18. 90
  19. 24
  20. 9.9
  21. 8.8
  22. 47
  23. 76
  24. 88
  25. 8.7
  26. 71
  27. 31
  28. 7.9
  29. 9.3
  30. 9.2
  31. 18
  32. 61
  33. 19
  34. 18
  35. 19
  36. 80
  37. 38
  38. 6.3
  39. 93
  40. 86

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