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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 947 · 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.√52 to 1 decimal place? (a) 7.2 (b) 7.4 (c) 7.3 (d) 7.5
  2. 2.Best estimate of 1204 ÷ 21? (a) 6000 (b) 600 (c) 60
  3. 3.√94 to 1 decimal place? (a) 9.9 (b) 10.0 (c) 9.8 (d) 9.7
  4. 4.Best estimate of 3724 ÷ 52? (a) 740 (b) 74 (c) 7400
  5. 5.Best estimate of 2340 ÷ 36? (a) 5900 (b) 59 (c) 590
  6. 6.√78 to 1 decimal place? (a) 8.8 (b) 9.1 (c) 9.0 (d) 8.9
  7. 7.√34 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.9 (d) 5.6
  8. 8.Best estimate of 4901 ÷ 71? (a) 70 (b) 700 (c) 7000
  9. 9.Best estimate of 2234 ÷ 72? (a) 320 (b) 32 (c) 3200
  10. 10.Best estimate of 1198 ÷ 48? (a) 2400 (b) 240 (c) 24
  11. 11.√87 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.4 (d) 9.1
  12. 12.Best estimate of 1773 ÷ 66? (a) 250 (b) 2500 (c) 25
  13. 13.Best estimate of 2091 ÷ 32? (a) 7000 (b) 700 (c) 70
  14. 14.√82 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 9.2 (d) 9.1
  15. 15.√96 to 1 decimal place? (a) 10.1 (b) 9.8 (c) 9.9 (d) 10.0
  16. 16.√92 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.5 (d) 9.6
  17. 17.Best estimate of 4189 ÷ 52? (a) 8400 (b) 840 (c) 84
  18. 18.√86 to 1 decimal place? (a) 9.0 (b) 9.2 (c) 9.1 (d) 9.3
  19. 19.Best estimate of 3886 ÷ 82? (a) 4900 (b) 490 (c) 49
  20. 20.Best estimate of 2314 ÷ 33? (a) 770 (b) 77 (c) 7700
  21. 21.Best estimate of 1242 ÷ 52? (a) 2500 (b) 25 (c) 250
  22. 22.Best estimate of 2792 ÷ 47? (a) 560 (b) 56 (c) 5600
  23. 23.Best estimate of 2052 ÷ 36? (a) 510 (b) 51 (c) 5100
  24. 24.Best estimate of 5448 ÷ 61? (a) 91 (b) 910 (c) 9100
  25. 25.Best estimate of 886 ÷ 68? (a) 1300 (b) 13 (c) 130
  26. 26.Best estimate of 1455 ÷ 58? (a) 2400 (b) 24 (c) 240
  27. 27.√85 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.2 (d) 9.3
  28. 28.√21 to 1 decimal place? (a) 4.5 (b) 4.3 (c) 4.4 (d) 4.6
  29. 29.√70 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.4 (d) 8.7
  30. 30.√50 to 1 decimal place? (a) 7.1 (b) 7.4 (c) 7.2 (d) 7.3
  31. 31.Best estimate of 2375 ÷ 77? (a) 300 (b) 30 (c) 3000
  32. 32.Best estimate of 1332 ÷ 52? (a) 2700 (b) 270 (c) 27
  33. 33.Best estimate of 7397 ÷ 82? (a) 920 (b) 9200 (c) 92
  34. 34.√38 to 1 decimal place? (a) 6.0 (b) 6.1 (c) 5.9 (d) 6.2
  35. 35.Best estimate of 5526 ÷ 58? (a) 920 (b) 92 (c) 9200
  36. 36.√30 to 1 decimal place? (a) 5.2 (b) 5.3 (c) 5.4 (d) 5.5
  37. 37.Best estimate of 1572 ÷ 21? (a) 79 (b) 7900 (c) 790
  38. 38.√31 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.6 (d) 5.9
  39. 39.√65 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.0 (d) 8.3
  40. 40.√20 to 1 decimal place? (a) 4.3 (b) 4.4 (c) 4.2 (d) 4.5

Answer key

  1. 7.2
  2. 60
  3. 9.7
  4. 74
  5. 59
  6. 8.8
  7. 5.8
  8. 70
  9. 32
  10. 24
  11. 9.3
  12. 25
  13. 70
  14. 9.1
  15. 9.8
  16. 9.6
  17. 84
  18. 9.3
  19. 49
  20. 77
  21. 25
  22. 56
  23. 51
  24. 91
  25. 13
  26. 24
  27. 9.2
  28. 4.6
  29. 8.4
  30. 7.1
  31. 30
  32. 27
  33. 92
  34. 6.2
  35. 92
  36. 5.5
  37. 79
  38. 5.6
  39. 8.1
  40. 4.5

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