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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 124 · 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.√78 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.5 (d) 8.8
  2. 2.√32 to 1 decimal place? (a) 5.9 (b) 5.8 (c) 5.6 (d) 5.7
  3. 3.Best estimate of 2563 ÷ 73? (a) 370 (b) 37 (c) 3700
  4. 4.Best estimate of 502 ÷ 21? (a) 250 (b) 2500 (c) 25
  5. 5.√84 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.3 (d) 9.2
  6. 6.√26 to 1 decimal place? (a) 5.2 (b) 5.1 (c) 5.3 (d) 5.0
  7. 7.√28 to 1 decimal place? (a) 5.4 (b) 5.6 (c) 5.3 (d) 5.5
  8. 8.Best estimate of 2307 ÷ 42? (a) 5800 (b) 580 (c) 58
  9. 9.√29 to 1 decimal place? (a) 5.4 (b) 5.2 (c) 5.3 (d) 5.1
  10. 10.√55 to 1 decimal place? (a) 7.2 (b) 7.3 (c) 7.4 (d) 7.5
  11. 11.√40 to 1 decimal place? (a) 6.6 (b) 6.4 (c) 6.5 (d) 6.3
  12. 12.√22 to 1 decimal place? (a) 4.9 (b) 4.8 (c) 4.7 (d) 5.0
  13. 13.√56 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.5 (d) 7.8
  14. 14.√96 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 10.0 (d) 9.7
  15. 15.√51 to 1 decimal place? (a) 7.0 (b) 7.2 (c) 6.9 (d) 7.1
  16. 16.√37 to 1 decimal place? (a) 6.1 (b) 6.0 (c) 6.2 (d) 5.9
  17. 17.√31 to 1 decimal place? (a) 5.6 (b) 5.8 (c) 5.9 (d) 5.7
  18. 18.Best estimate of 480 ÷ 36? (a) 12 (b) 1200 (c) 120
  19. 19.Best estimate of 2158 ÷ 34? (a) 7200 (b) 72 (c) 720
  20. 20.Best estimate of 4628 ÷ 87? (a) 510 (b) 5100 (c) 51
  21. 21.Best estimate of 1020 ÷ 24? (a) 5100 (b) 510 (c) 51
  22. 22.√82 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 9.2 (d) 8.9
  23. 23.√71 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.3 (d) 8.6
  24. 24.Best estimate of 4400 ÷ 83? (a) 55 (b) 550 (c) 5500
  25. 25.Best estimate of 1508 ÷ 73? (a) 2200 (b) 220 (c) 22
  26. 26.Best estimate of 2289 ÷ 83? (a) 2900 (b) 290 (c) 29
  27. 27.√69 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.0 (d) 8.1
  28. 28.√35 to 1 decimal place? (a) 5.9 (b) 5.6 (c) 5.8 (d) 5.7
  29. 29.√34 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.9 (d) 6.0
  30. 30.Best estimate of 1608 ÷ 81? (a) 2000 (b) 200 (c) 20
  31. 31.Best estimate of 551 ÷ 21? (a) 28 (b) 280 (c) 2800
  32. 32.Best estimate of 5444 ÷ 84? (a) 680 (b) 68 (c) 6800
  33. 33.Best estimate of 4401 ÷ 66? (a) 630 (b) 63 (c) 6300
  34. 34.Best estimate of 1653 ÷ 26? (a) 550 (b) 5500 (c) 55
  35. 35.Best estimate of 1820 ÷ 67? (a) 26 (b) 260 (c) 2600
  36. 36.Best estimate of 1618 ÷ 39? (a) 4000 (b) 40 (c) 400
  37. 37.Best estimate of 3024 ÷ 42? (a) 760 (b) 76 (c) 7600
  38. 38.√58 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.3 (d) 7.4
  39. 39.√80 to 1 decimal place? (a) 9.1 (b) 8.9 (c) 8.8 (d) 9.0
  40. 40.√94 to 1 decimal place? (a) 9.7 (b) 9.5 (c) 9.6 (d) 9.8

Answer key

  1. 8.8
  2. 5.7
  3. 37
  4. 25
  5. 9.2
  6. 5.1
  7. 5.3
  8. 58
  9. 5.4
  10. 7.4
  11. 6.3
  12. 4.7
  13. 7.5
  14. 9.8
  15. 7.1
  16. 6.1
  17. 5.6
  18. 12
  19. 72
  20. 51
  21. 51
  22. 9.1
  23. 8.4
  24. 55
  25. 22
  26. 29
  27. 8.3
  28. 5.9
  29. 5.8
  30. 20
  31. 28
  32. 68
  33. 63
  34. 55
  35. 26
  36. 40
  37. 76
  38. 7.6
  39. 8.9
  40. 9.7

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