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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 119 · 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.√58 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.5 (d) 7.4
  2. 2.√50 to 1 decimal place? (a) 7.1 (b) 7.3 (c) 7.4 (d) 7.2
  3. 3.√61 to 1 decimal place? (a) 7.7 (b) 7.9 (c) 8.0 (d) 7.8
  4. 4.√82 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 9.2 (d) 9.1
  5. 5.√28 to 1 decimal place? (a) 5.3 (b) 5.6 (c) 5.4 (d) 5.5
  6. 6.Best estimate of 3499 ÷ 46? (a) 70 (b) 700 (c) 7000
  7. 7.√70 to 1 decimal place? (a) 8.5 (b) 8.7 (c) 8.4 (d) 8.6
  8. 8.Best estimate of 4335 ÷ 63? (a) 7200 (b) 720 (c) 72
  9. 9.Best estimate of 5781 ÷ 68? (a) 830 (b) 8300 (c) 83
  10. 10.√84 to 1 decimal place? (a) 9.4 (b) 9.2 (c) 9.3 (d) 9.5
  11. 11.Best estimate of 3925 ÷ 72? (a) 5600 (b) 56 (c) 560
  12. 12.Best estimate of 1489 ÷ 31? (a) 5000 (b) 50 (c) 500
  13. 13.√34 to 1 decimal place? (a) 5.8 (b) 5.6 (c) 5.9 (d) 5.7
  14. 14.√79 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.7 (d) 8.6
  15. 15.Best estimate of 1055 ÷ 67? (a) 15 (b) 1500 (c) 150
  16. 16.√47 to 1 decimal place? (a) 7.2 (b) 7.0 (c) 7.1 (d) 6.9
  17. 17.Best estimate of 4200 ÷ 71? (a) 6000 (b) 60 (c) 600
  18. 18.Best estimate of 4787 ÷ 72? (a) 680 (b) 6800 (c) 68
  19. 19.√55 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.4 (d) 7.3
  20. 20.Best estimate of 5712 ÷ 66? (a) 820 (b) 82 (c) 8200
  21. 21.Best estimate of 3802 ÷ 46? (a) 7600 (b) 760 (c) 76
  22. 22.Best estimate of 851 ÷ 52? (a) 17 (b) 170 (c) 1700
  23. 23.√24 to 1 decimal place? (a) 4.8 (b) 4.9 (c) 5.0 (d) 5.1
  24. 24.√31 to 1 decimal place? (a) 5.6 (b) 5.5 (c) 5.3 (d) 5.4
  25. 25.Best estimate of 5659 ÷ 62? (a) 940 (b) 9400 (c) 94
  26. 26.Best estimate of 2364 ÷ 48? (a) 4700 (b) 470 (c) 47
  27. 27.√90 to 1 decimal place? (a) 9.5 (b) 9.7 (c) 9.4 (d) 9.6
  28. 28.√80 to 1 decimal place? (a) 8.9 (b) 8.7 (c) 9.0 (d) 8.8
  29. 29.Best estimate of 3546 ÷ 53? (a) 710 (b) 71 (c) 7100
  30. 30.√74 to 1 decimal place? (a) 8.7 (b) 8.4 (c) 8.6 (d) 8.5
  31. 31.Best estimate of 1541 ÷ 73? (a) 22 (b) 220 (c) 2200
  32. 32.√96 to 1 decimal place? (a) 9.7 (b) 9.9 (c) 9.6 (d) 9.8
  33. 33.√71 to 1 decimal place? (a) 8.6 (b) 8.3 (c) 8.4 (d) 8.5
  34. 34.√46 to 1 decimal place? (a) 6.7 (b) 6.9 (c) 6.8 (d) 7.0
  35. 35.Best estimate of 2642 ÷ 29? (a) 8800 (b) 880 (c) 88
  36. 36.Best estimate of 4430 ÷ 72? (a) 6300 (b) 63 (c) 630
  37. 37.√98 to 1 decimal place? (a) 10.0 (b) 9.7 (c) 9.8 (d) 9.9
  38. 38.√77 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.8 (d) 8.9
  39. 39.√72 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.5 (d) 8.4
  40. 40.Best estimate of 3263 ÷ 53? (a) 65 (b) 6500 (c) 650

Answer key

  1. 7.6
  2. 7.1
  3. 7.8
  4. 9.1
  5. 5.3
  6. 70
  7. 8.4
  8. 72
  9. 83
  10. 9.2
  11. 56
  12. 50
  13. 5.8
  14. 8.9
  15. 15
  16. 6.9
  17. 60
  18. 68
  19. 7.4
  20. 82
  21. 76
  22. 17
  23. 4.9
  24. 5.6
  25. 94
  26. 47
  27. 9.5
  28. 8.9
  29. 71
  30. 8.6
  31. 22
  32. 9.8
  33. 8.4
  34. 6.8
  35. 88
  36. 63
  37. 9.9
  38. 8.8
  39. 8.5
  40. 65

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