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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 180 · 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.√92 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 9.6 (d) 9.8
  2. 2.√24 to 1 decimal place? (a) 4.9 (b) 5.1 (c) 4.8 (d) 5.0
  3. 3.Best estimate of 3307 ÷ 56? (a) 550 (b) 5500 (c) 55
  4. 4.√32 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.5 (d) 5.6
  5. 5.√61 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 7.6 (d) 7.9
  6. 6.Best estimate of 4882 ÷ 66? (a) 70 (b) 700 (c) 7000
  7. 7.Best estimate of 578 ÷ 44? (a) 140 (b) 1400 (c) 14
  8. 8.Best estimate of 457 ÷ 36? (a) 11 (b) 1100 (c) 110
  9. 9.Best estimate of 4783 ÷ 52? (a) 960 (b) 9600 (c) 96
  10. 10.Best estimate of 1877 ÷ 64? (a) 310 (b) 31 (c) 3100
  11. 11.√48 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 7.1 (d) 6.8
  12. 12.Best estimate of 2339 ÷ 77? (a) 2900 (b) 29 (c) 290
  13. 13.Best estimate of 1683 ÷ 67? (a) 24 (b) 240 (c) 2400
  14. 14.√26 to 1 decimal place? (a) 5.1 (b) 5.3 (c) 5.2 (d) 5.0
  15. 15.Best estimate of 823 ÷ 27? (a) 27 (b) 2700 (c) 270
  16. 16.√50 to 1 decimal place? (a) 7.0 (b) 6.9 (c) 7.1 (d) 7.2
  17. 17.Best estimate of 815 ÷ 34? (a) 270 (b) 27 (c) 2700
  18. 18.√75 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.8 (d) 8.5
  19. 19.Best estimate of 1077 ÷ 53? (a) 22 (b) 220 (c) 2200
  20. 20.Best estimate of 2181 ÷ 39? (a) 55 (b) 5500 (c) 550
  21. 21.Best estimate of 1064 ÷ 56? (a) 1800 (b) 180 (c) 18
  22. 22.√56 to 1 decimal place? (a) 7.3 (b) 7.4 (c) 7.5 (d) 7.2
  23. 23.Best estimate of 2465 ÷ 41? (a) 6200 (b) 620 (c) 62
  24. 24.√40 to 1 decimal place? (a) 6.4 (b) 6.3 (c) 6.5 (d) 6.2
  25. 25.Best estimate of 775 ÷ 39? (a) 19 (b) 1900 (c) 190
  26. 26.√58 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 7.7 (d) 7.6
  27. 27.√84 to 1 decimal place? (a) 8.9 (b) 9.2 (c) 9.1 (d) 9.0
  28. 28.√78 to 1 decimal place? (a) 8.9 (b) 9.1 (c) 8.8 (d) 9.0
  29. 29.Best estimate of 1693 ÷ 76? (a) 21 (b) 210 (c) 2100
  30. 30.Best estimate of 1851 ÷ 77? (a) 2300 (b) 23 (c) 230
  31. 31.Best estimate of 3557 ÷ 52? (a) 7100 (b) 710 (c) 71
  32. 32.Best estimate of 5075 ÷ 86? (a) 560 (b) 56 (c) 5600
  33. 33.√59 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 7.7 (d) 7.8
  34. 34.Best estimate of 7374 ÷ 87? (a) 820 (b) 8200 (c) 82
  35. 35.Best estimate of 1793 ÷ 42? (a) 450 (b) 4500 (c) 45
  36. 36.√82 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.3 (d) 9.0
  37. 37.Best estimate of 4048 ÷ 58? (a) 670 (b) 6700 (c) 67
  38. 38.Best estimate of 1842 ÷ 32? (a) 610 (b) 6100 (c) 61
  39. 39.√98 to 1 decimal place? (a) 10.1 (b) 10.0 (c) 9.9 (d) 10.2
  40. 40.√67 to 1 decimal place? (a) 8.2 (b) 8.5 (c) 8.4 (d) 8.3

Answer key

  1. 9.6
  2. 4.9
  3. 55
  4. 5.7
  5. 7.8
  6. 70
  7. 14
  8. 11
  9. 96
  10. 31
  11. 6.9
  12. 29
  13. 24
  14. 5.1
  15. 27
  16. 7.1
  17. 27
  18. 8.7
  19. 22
  20. 55
  21. 18
  22. 7.5
  23. 62
  24. 6.3
  25. 19
  26. 7.6
  27. 9.2
  28. 8.8
  29. 21
  30. 23
  31. 71
  32. 56
  33. 7.7
  34. 82
  35. 45
  36. 9.1
  37. 67
  38. 61
  39. 9.9
  40. 8.2

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