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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 143 · 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.√20 to 1 decimal place? (a) 4.5 (b) 4.6 (c) 4.7 (d) 4.8
  2. 2.√80 to 1 decimal place? (a) 9.1 (b) 8.8 (c) 9.0 (d) 8.9
  3. 3.Best estimate of 3703 ÷ 58? (a) 620 (b) 62 (c) 6200
  4. 4.Best estimate of 3764 ÷ 44? (a) 940 (b) 9400 (c) 94
  5. 5.√45 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.9 (d) 6.8
  6. 6.Best estimate of 2283 ÷ 26? (a) 760 (b) 7600 (c) 76
  7. 7.√21 to 1 decimal place? (a) 4.7 (b) 4.8 (c) 4.5 (d) 4.6
  8. 8.√92 to 1 decimal place? (a) 9.6 (b) 9.5 (c) 9.3 (d) 9.4
  9. 9.√48 to 1 decimal place? (a) 6.8 (b) 6.7 (c) 6.9 (d) 6.6
  10. 10.Best estimate of 3812 ÷ 66? (a) 5400 (b) 540 (c) 54
  11. 11.√31 to 1 decimal place? (a) 5.9 (b) 5.8 (c) 5.6 (d) 5.7
  12. 12.√75 to 1 decimal place? (a) 8.7 (b) 8.5 (c) 8.6 (d) 8.4
  13. 13.Best estimate of 1897 ÷ 31? (a) 6300 (b) 630 (c) 63
  14. 14.Best estimate of 1257 ÷ 31? (a) 42 (b) 4200 (c) 420
  15. 15.Best estimate of 4667 ÷ 81? (a) 5800 (b) 580 (c) 58
  16. 16.√42 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.8 (d) 6.7
  17. 17.Best estimate of 3172 ÷ 66? (a) 450 (b) 45 (c) 4500
  18. 18.√58 to 1 decimal place? (a) 7.3 (b) 7.5 (c) 7.6 (d) 7.4
  19. 19.Best estimate of 3921 ÷ 52? (a) 7800 (b) 780 (c) 78
  20. 20.Best estimate of 6582 ÷ 81? (a) 820 (b) 82 (c) 8200
  21. 21.Best estimate of 2116 ÷ 86? (a) 240 (b) 24 (c) 2400
  22. 22.√71 to 1 decimal place? (a) 8.7 (b) 8.5 (c) 8.6 (d) 8.4
  23. 23.Best estimate of 2984 ÷ 81? (a) 3700 (b) 37 (c) 370
  24. 24.√40 to 1 decimal place? (a) 6.0 (b) 6.3 (c) 6.1 (d) 6.2
  25. 25.√56 to 1 decimal place? (a) 7.5 (b) 7.7 (c) 7.8 (d) 7.6
  26. 26.Best estimate of 2504 ÷ 78? (a) 310 (b) 3100 (c) 31
  27. 27.Best estimate of 2651 ÷ 78? (a) 3300 (b) 330 (c) 33
  28. 28.Best estimate of 4370 ÷ 77? (a) 55 (b) 5500 (c) 550
  29. 29.Best estimate of 1283 ÷ 21? (a) 64 (b) 6400 (c) 640
  30. 30.√88 to 1 decimal place? (a) 9.7 (b) 9.4 (c) 9.5 (d) 9.6
  31. 31.Best estimate of 6073 ÷ 66? (a) 870 (b) 8700 (c) 87
  32. 32.√98 to 1 decimal place? (a) 9.8 (b) 10.0 (c) 9.7 (d) 9.9
  33. 33.√82 to 1 decimal place? (a) 9.1 (b) 8.9 (c) 8.8 (d) 9.0
  34. 34.Best estimate of 1963 ÷ 52? (a) 3900 (b) 390 (c) 39
  35. 35.Best estimate of 3698 ÷ 73? (a) 5300 (b) 530 (c) 53
  36. 36.Best estimate of 1501 ÷ 23? (a) 75 (b) 750 (c) 7500
  37. 37.Best estimate of 950 ÷ 46? (a) 19 (b) 190 (c) 1900
  38. 38.Best estimate of 699 ÷ 46? (a) 14 (b) 1400 (c) 140
  39. 39.√74 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.7 (d) 8.6
  40. 40.√94 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 9.6 (d) 9.8

Answer key

  1. 4.5
  2. 8.9
  3. 62
  4. 94
  5. 6.7
  6. 76
  7. 4.6
  8. 9.6
  9. 6.9
  10. 54
  11. 5.6
  12. 8.7
  13. 63
  14. 42
  15. 58
  16. 6.5
  17. 45
  18. 7.6
  19. 78
  20. 82
  21. 24
  22. 8.4
  23. 37
  24. 6.3
  25. 7.5
  26. 31
  27. 33
  28. 55
  29. 64
  30. 9.4
  31. 87
  32. 9.9
  33. 9.1
  34. 39
  35. 53
  36. 75
  37. 19
  38. 14
  39. 8.6
  40. 9.7

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