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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 821 · 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.√21 to 1 decimal place? (a) 4.6 (b) 4.8 (c) 4.5 (d) 4.7
  2. 2.Best estimate of 4725 ÷ 56? (a) 790 (b) 7900 (c) 79
  3. 3.√48 to 1 decimal place? (a) 7.0 (b) 6.9 (c) 7.1 (d) 7.2
  4. 4.√76 to 1 decimal place? (a) 8.7 (b) 8.9 (c) 8.8 (d) 8.6
  5. 5.√65 to 1 decimal place? (a) 8.1 (b) 8.4 (c) 8.3 (d) 8.2
  6. 6.√98 to 1 decimal place? (a) 10.0 (b) 9.8 (c) 9.7 (d) 9.9
  7. 7.Best estimate of 5089 ÷ 56? (a) 8500 (b) 850 (c) 85
  8. 8.Best estimate of 6490 ÷ 89? (a) 7200 (b) 72 (c) 720
  9. 9.√37 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.1 (d) 6.2
  10. 10.Best estimate of 831 ÷ 69? (a) 120 (b) 1200 (c) 12
  11. 11.√92 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 9.6 (d) 9.7
  12. 12.Best estimate of 4053 ÷ 86? (a) 450 (b) 45 (c) 4500
  13. 13.√61 to 1 decimal place? (a) 7.8 (b) 7.5 (c) 7.7 (d) 7.6
  14. 14.Best estimate of 5029 ÷ 84? (a) 630 (b) 6300 (c) 63
  15. 15.√94 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.9 (d) 9.8
  16. 16.√27 to 1 decimal place? (a) 5.0 (b) 5.1 (c) 5.2 (d) 5.3
  17. 17.√89 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.7 (d) 9.6
  18. 18.Best estimate of 4555 ÷ 63? (a) 7600 (b) 760 (c) 76
  19. 19.√26 to 1 decimal place? (a) 5.0 (b) 4.9 (c) 5.1 (d) 4.8
  20. 20.Best estimate of 3107 ÷ 62? (a) 520 (b) 5200 (c) 52
  21. 21.√35 to 1 decimal place? (a) 6.1 (b) 6.0 (c) 5.8 (d) 5.9
  22. 22.√43 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 6.6 (d) 6.7
  23. 23.Best estimate of 2931 ÷ 86? (a) 330 (b) 33 (c) 3300
  24. 24.√88 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.1 (d) 9.4
  25. 25.Best estimate of 3150 ÷ 68? (a) 450 (b) 45 (c) 4500
  26. 26.√51 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 7.3 (d) 7.0
  27. 27.Best estimate of 955 ÷ 53? (a) 19 (b) 1900 (c) 190
  28. 28.Best estimate of 1321 ÷ 64? (a) 2200 (b) 220 (c) 22
  29. 29.√58 to 1 decimal place? (a) 7.6 (b) 7.3 (c) 7.4 (d) 7.5
  30. 30.Best estimate of 1818 ÷ 36? (a) 450 (b) 4500 (c) 45
  31. 31.Best estimate of 1595 ÷ 53? (a) 32 (b) 320 (c) 3200
  32. 32.Best estimate of 592 ÷ 22? (a) 30 (b) 300 (c) 3000
  33. 33.Best estimate of 6733 ÷ 78? (a) 840 (b) 8400 (c) 84
  34. 34.√55 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.2 (d) 7.3
  35. 35.√50 to 1 decimal place? (a) 7.2 (b) 7.4 (c) 7.1 (d) 7.3
  36. 36.Best estimate of 2826 ÷ 83? (a) 350 (b) 3500 (c) 35
  37. 37.Best estimate of 3183 ÷ 42? (a) 8000 (b) 80 (c) 800
  38. 38.√40 to 1 decimal place? (a) 6.1 (b) 6.2 (c) 6.3 (d) 6.4
  39. 39.√74 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.8 (d) 8.9
  40. 40.Best estimate of 2756 ÷ 43? (a) 69 (b) 6900 (c) 690

Answer key

  1. 4.6
  2. 79
  3. 6.9
  4. 8.7
  5. 8.1
  6. 9.9
  7. 85
  8. 72
  9. 6.1
  10. 12
  11. 9.6
  12. 45
  13. 7.8
  14. 63
  15. 9.7
  16. 5.2
  17. 9.4
  18. 76
  19. 5.1
  20. 52
  21. 5.9
  22. 6.6
  23. 33
  24. 9.4
  25. 45
  26. 7.1
  27. 19
  28. 22
  29. 7.6
  30. 45
  31. 32
  32. 30
  33. 84
  34. 7.4
  35. 7.1
  36. 35
  37. 80
  38. 6.3
  39. 8.6
  40. 69

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