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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 932 · 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 5567 ÷ 83? (a) 700 (b) 7000 (c) 70
  2. 2.√27 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 4.9 (d) 5.2
  3. 3.√74 to 1 decimal place? (a) 8.7 (b) 8.5 (c) 8.4 (d) 8.6
  4. 4.Best estimate of 4775 ÷ 52? (a) 9600 (b) 96 (c) 960
  5. 5.√44 to 1 decimal place? (a) 6.5 (b) 6.8 (c) 6.6 (d) 6.7
  6. 6.Best estimate of 6623 ÷ 83? (a) 83 (b) 830 (c) 8300
  7. 7.√40 to 1 decimal place? (a) 6.3 (b) 6.1 (c) 6.0 (d) 6.2
  8. 8.Best estimate of 3103 ÷ 38? (a) 780 (b) 7800 (c) 78
  9. 9.Best estimate of 2713 ÷ 31? (a) 900 (b) 9000 (c) 90
  10. 10.√85 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.2 (d) 9.3
  11. 11.√79 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.6 (d) 8.9
  12. 12.√94 to 1 decimal place? (a) 9.8 (b) 9.7 (c) 9.6 (d) 9.9
  13. 13.√51 to 1 decimal place? (a) 6.9 (b) 7.2 (c) 7.1 (d) 7.0
  14. 14.Best estimate of 3277 ÷ 36? (a) 820 (b) 8200 (c) 82
  15. 15.Best estimate of 967 ÷ 23? (a) 48 (b) 4800 (c) 480
  16. 16.√26 to 1 decimal place? (a) 5.2 (b) 5.1 (c) 4.9 (d) 5.0
  17. 17.√72 to 1 decimal place? (a) 8.5 (b) 8.3 (c) 8.2 (d) 8.4
  18. 18.√71 to 1 decimal place? (a) 8.7 (b) 8.5 (c) 8.6 (d) 8.4
  19. 19.√92 to 1 decimal place? (a) 9.5 (b) 9.3 (c) 9.4 (d) 9.6
  20. 20.√30 to 1 decimal place? (a) 5.7 (b) 5.5 (c) 5.4 (d) 5.6
  21. 21.Best estimate of 6175 ÷ 83? (a) 770 (b) 7700 (c) 77
  22. 22.√41 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.4 (d) 6.7
  23. 23.Best estimate of 1583 ÷ 52? (a) 32 (b) 320 (c) 3200
  24. 24.√48 to 1 decimal place? (a) 6.9 (b) 6.6 (c) 6.8 (d) 6.7
  25. 25.√61 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 8.1 (d) 7.8
  26. 26.Best estimate of 674 ÷ 21? (a) 34 (b) 340 (c) 3400
  27. 27.√34 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 6.0 (d) 5.9
  28. 28.Best estimate of 2038 ÷ 33? (a) 680 (b) 6800 (c) 68
  29. 29.Best estimate of 6568 ÷ 76? (a) 820 (b) 82 (c) 8200
  30. 30.√98 to 1 decimal place? (a) 9.9 (b) 9.8 (c) 10.0 (d) 10.1
  31. 31.Best estimate of 1462 ÷ 83? (a) 1800 (b) 18 (c) 180
  32. 32.Best estimate of 3301 ÷ 42? (a) 8300 (b) 830 (c) 83
  33. 33.Best estimate of 3677 ÷ 56? (a) 6100 (b) 61 (c) 610
  34. 34.Best estimate of 2966 ÷ 76? (a) 3700 (b) 37 (c) 370
  35. 35.√63 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 8.2 (d) 7.9
  36. 36.√35 to 1 decimal place? (a) 5.6 (b) 5.8 (c) 5.9 (d) 5.7
  37. 37.√23 to 1 decimal place? (a) 4.8 (b) 4.5 (c) 4.6 (d) 4.7
  38. 38.Best estimate of 1403 ÷ 56? (a) 23 (b) 230 (c) 2300
  39. 39.Best estimate of 2446 ÷ 36? (a) 6100 (b) 61 (c) 610
  40. 40.Best estimate of 1536 ÷ 32? (a) 5100 (b) 51 (c) 510

Answer key

  1. 70
  2. 5.2
  3. 8.6
  4. 96
  5. 6.6
  6. 83
  7. 6.3
  8. 78
  9. 90
  10. 9.2
  11. 8.9
  12. 9.7
  13. 7.1
  14. 82
  15. 48
  16. 5.1
  17. 8.5
  18. 8.4
  19. 9.6
  20. 5.5
  21. 77
  22. 6.4
  23. 32
  24. 6.9
  25. 7.8
  26. 34
  27. 5.8
  28. 68
  29. 82
  30. 9.9
  31. 18
  32. 83
  33. 61
  34. 37
  35. 7.9
  36. 5.9
  37. 4.8
  38. 23
  39. 61
  40. 51

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