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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 529 · 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.√62 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 7.9 (d) 8.0
  2. 2.Best estimate of 3064 ÷ 58? (a) 510 (b) 5100 (c) 51
  3. 3.Best estimate of 2500 ÷ 36? (a) 630 (b) 6300 (c) 63
  4. 4.Best estimate of 1167 ÷ 71? (a) 170 (b) 1700 (c) 17
  5. 5.Best estimate of 2340 ÷ 32? (a) 78 (b) 780 (c) 7800
  6. 6.Best estimate of 5758 ÷ 87? (a) 64 (b) 640 (c) 6400
  7. 7.√70 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.5 (d) 8.6
  8. 8.√46 to 1 decimal place? (a) 6.9 (b) 6.6 (c) 6.8 (d) 6.7
  9. 9.Best estimate of 5903 ÷ 86? (a) 6600 (b) 66 (c) 660
  10. 10.Best estimate of 3057 ÷ 63? (a) 51 (b) 5100 (c) 510
  11. 11.Best estimate of 2390 ÷ 73? (a) 340 (b) 3400 (c) 34
  12. 12.√76 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.7 (d) 9.0
  13. 13.√40 to 1 decimal place? (a) 6.4 (b) 6.3 (c) 6.5 (d) 6.6
  14. 14.√22 to 1 decimal place? (a) 4.6 (b) 4.5 (c) 4.7 (d) 4.4
  15. 15.Best estimate of 6573 ÷ 76? (a) 82 (b) 8200 (c) 820
  16. 16.Best estimate of 1276 ÷ 31? (a) 43 (b) 4300 (c) 430
  17. 17.√69 to 1 decimal place? (a) 8.4 (b) 8.2 (c) 8.1 (d) 8.3
  18. 18.√26 to 1 decimal place? (a) 5.2 (b) 5.1 (c) 5.4 (d) 5.3
  19. 19.Best estimate of 2254 ÷ 82? (a) 280 (b) 2800 (c) 28
  20. 20.√74 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.7 (d) 8.8
  21. 21.√61 to 1 decimal place? (a) 7.9 (b) 7.7 (c) 7.8 (d) 7.6
  22. 22.Best estimate of 2603 ÷ 29? (a) 8700 (b) 87 (c) 870
  23. 23.Best estimate of 3171 ÷ 47? (a) 63 (b) 630 (c) 6300
  24. 24.√92 to 1 decimal place? (a) 9.9 (b) 9.6 (c) 9.7 (d) 9.8
  25. 25.√29 to 1 decimal place? (a) 5.2 (b) 5.4 (c) 5.3 (d) 5.1
  26. 26.Best estimate of 1923 ÷ 64? (a) 320 (b) 3200 (c) 32
  27. 27.Best estimate of 6017 ÷ 88? (a) 670 (b) 6700 (c) 67
  28. 28.Best estimate of 1312 ÷ 22? (a) 660 (b) 6600 (c) 66
  29. 29.√89 to 1 decimal place? (a) 9.2 (b) 9.5 (c) 9.3 (d) 9.4
  30. 30.√30 to 1 decimal place? (a) 5.7 (b) 5.5 (c) 5.6 (d) 5.8
  31. 31.Best estimate of 504 ÷ 23? (a) 25 (b) 2500 (c) 250
  32. 32.Best estimate of 2514 ÷ 38? (a) 630 (b) 6300 (c) 63
  33. 33.Best estimate of 1008 ÷ 33? (a) 340 (b) 3400 (c) 34
  34. 34.Best estimate of 1340 ÷ 36? (a) 340 (b) 3400 (c) 34
  35. 35.√31 to 1 decimal place? (a) 5.8 (b) 5.5 (c) 5.6 (d) 5.7
  36. 36.Best estimate of 1649 ÷ 28? (a) 5500 (b) 550 (c) 55
  37. 37.√58 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.8 (d) 7.7
  38. 38.√86 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 9.2 (d) 9.3
  39. 39.Best estimate of 4743 ÷ 57? (a) 790 (b) 7900 (c) 79
  40. 40.√75 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.7 (d) 8.4

Answer key

  1. 7.9
  2. 51
  3. 63
  4. 17
  5. 78
  6. 64
  7. 8.4
  8. 6.8
  9. 66
  10. 51
  11. 34
  12. 8.7
  13. 6.3
  14. 4.7
  15. 82
  16. 43
  17. 8.3
  18. 5.1
  19. 28
  20. 8.6
  21. 7.8
  22. 87
  23. 63
  24. 9.6
  25. 5.4
  26. 32
  27. 67
  28. 66
  29. 9.4
  30. 5.5
  31. 25
  32. 63
  33. 34
  34. 34
  35. 5.6
  36. 55
  37. 7.6
  38. 9.3
  39. 79
  40. 8.7

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