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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 880 · 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 6543 ÷ 76? (a) 82 (b) 820 (c) 8200
  2. 2.√24 to 1 decimal place? (a) 5.0 (b) 5.1 (c) 5.2 (d) 4.9
  3. 3.√75 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.5 (d) 8.4
  4. 4.√21 to 1 decimal place? (a) 4.5 (b) 4.4 (c) 4.3 (d) 4.6
  5. 5.Best estimate of 1111 ÷ 74? (a) 16 (b) 1600 (c) 160
  6. 6.√88 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.3 (d) 9.2
  7. 7.Best estimate of 3010 ÷ 54? (a) 60 (b) 600 (c) 6000
  8. 8.Best estimate of 3039 ÷ 67? (a) 430 (b) 43 (c) 4300
  9. 9.Best estimate of 3122 ÷ 48? (a) 620 (b) 6200 (c) 62
  10. 10.√45 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.6 (d) 6.7
  11. 11.Best estimate of 868 ÷ 36? (a) 220 (b) 2200 (c) 22
  12. 12.Best estimate of 2389 ÷ 68? (a) 34 (b) 340 (c) 3400
  13. 13.√79 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 8.7 (d) 8.8
  14. 14.√50 to 1 decimal place? (a) 7.1 (b) 6.9 (c) 7.2 (d) 7.0
  15. 15.Best estimate of 3771 ÷ 42? (a) 940 (b) 94 (c) 9400
  16. 16.Best estimate of 4570 ÷ 73? (a) 650 (b) 6500 (c) 65
  17. 17.√43 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.5 (d) 6.6
  18. 18.Best estimate of 5625 ÷ 67? (a) 8000 (b) 80 (c) 800
  19. 19.Best estimate of 2045 ÷ 47? (a) 41 (b) 4100 (c) 410
  20. 20.Best estimate of 1946 ÷ 42? (a) 490 (b) 4900 (c) 49
  21. 21.Best estimate of 1675 ÷ 78? (a) 2100 (b) 210 (c) 21
  22. 22.Best estimate of 5484 ÷ 76? (a) 690 (b) 69 (c) 6900
  23. 23.Best estimate of 3457 ÷ 74? (a) 49 (b) 490 (c) 4900
  24. 24.√98 to 1 decimal place? (a) 10.1 (b) 10.0 (c) 9.9 (d) 9.8
  25. 25.√37 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.3 (d) 6.1
  26. 26.Best estimate of 1142 ÷ 64? (a) 19 (b) 190 (c) 1900
  27. 27.Best estimate of 4099 ÷ 52? (a) 820 (b) 82 (c) 8200
  28. 28.Best estimate of 4704 ÷ 69? (a) 67 (b) 670 (c) 6700
  29. 29.Best estimate of 6221 ÷ 79? (a) 780 (b) 7800 (c) 78
  30. 30.Best estimate of 6334 ÷ 83? (a) 790 (b) 7900 (c) 79
  31. 31.Best estimate of 4318 ÷ 56? (a) 7200 (b) 72 (c) 720
  32. 32.√61 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 7.5 (d) 7.6
  33. 33.Best estimate of 3797 ÷ 63? (a) 630 (b) 63 (c) 6300
  34. 34.Best estimate of 4048 ÷ 68? (a) 5800 (b) 58 (c) 580
  35. 35.Best estimate of 1152 ÷ 36? (a) 29 (b) 290 (c) 2900
  36. 36.Best estimate of 951 ÷ 52? (a) 1900 (b) 190 (c) 19
  37. 37.Best estimate of 2131 ÷ 27? (a) 71 (b) 7100 (c) 710
  38. 38.√55 to 1 decimal place? (a) 7.2 (b) 7.3 (c) 7.4 (d) 7.1
  39. 39.√78 to 1 decimal place? (a) 8.5 (b) 8.8 (c) 8.6 (d) 8.7
  40. 40.Best estimate of 3790 ÷ 47? (a) 760 (b) 7600 (c) 76

Answer key

  1. 82
  2. 4.9
  3. 8.7
  4. 4.6
  5. 16
  6. 9.4
  7. 60
  8. 43
  9. 62
  10. 6.7
  11. 22
  12. 34
  13. 8.9
  14. 7.1
  15. 94
  16. 65
  17. 6.6
  18. 80
  19. 41
  20. 49
  21. 21
  22. 69
  23. 49
  24. 9.9
  25. 6.1
  26. 19
  27. 82
  28. 67
  29. 78
  30. 79
  31. 72
  32. 7.8
  33. 63
  34. 58
  35. 29
  36. 19
  37. 71
  38. 7.4
  39. 8.8
  40. 76

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