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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 718 · 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.√51 to 1 decimal place? (a) 7.3 (b) 7.1 (c) 7.2 (d) 7.4
  2. 2.√34 to 1 decimal place? (a) 5.8 (b) 6.0 (c) 6.1 (d) 5.9
  3. 3.Best estimate of 4218 ÷ 71? (a) 6000 (b) 600 (c) 60
  4. 4.√24 to 1 decimal place? (a) 4.7 (b) 4.9 (c) 4.6 (d) 4.8
  5. 5.Best estimate of 791 ÷ 56? (a) 130 (b) 1300 (c) 13
  6. 6.Best estimate of 2376 ÷ 46? (a) 4800 (b) 480 (c) 48
  7. 7.Best estimate of 1593 ÷ 72? (a) 2300 (b) 230 (c) 23
  8. 8.√53 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 7.2 (d) 7.3
  9. 9.Best estimate of 1417 ÷ 64? (a) 24 (b) 2400 (c) 240
  10. 10.Best estimate of 3708 ÷ 56? (a) 6200 (b) 62 (c) 620
  11. 11.Best estimate of 4257 ÷ 74? (a) 610 (b) 61 (c) 6100
  12. 12.Best estimate of 1624 ÷ 48? (a) 3200 (b) 32 (c) 320
  13. 13.√65 to 1 decimal place? (a) 7.9 (b) 8.1 (c) 8.2 (d) 8.0
  14. 14.√38 to 1 decimal place? (a) 6.3 (b) 6.2 (c) 6.5 (d) 6.4
  15. 15.Best estimate of 330 ÷ 24? (a) 17 (b) 170 (c) 1700
  16. 16.Best estimate of 8352 ÷ 89? (a) 93 (b) 930 (c) 9300
  17. 17.√37 to 1 decimal place? (a) 6.4 (b) 6.1 (c) 6.2 (d) 6.3
  18. 18.Best estimate of 4242 ÷ 73? (a) 610 (b) 61 (c) 6100
  19. 19.√52 to 1 decimal place? (a) 7.2 (b) 7.3 (c) 7.0 (d) 7.1
  20. 20.√41 to 1 decimal place? (a) 6.1 (b) 6.2 (c) 6.3 (d) 6.4
  21. 21.√66 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 8.3 (d) 8.2
  22. 22.Best estimate of 685 ÷ 56? (a) 110 (b) 11 (c) 1100
  23. 23.√67 to 1 decimal place? (a) 8.2 (b) 8.5 (c) 8.3 (d) 8.4
  24. 24.Best estimate of 3731 ÷ 48? (a) 75 (b) 7500 (c) 750
  25. 25.Best estimate of 3251 ÷ 62? (a) 54 (b) 5400 (c) 540
  26. 26.Best estimate of 4230 ÷ 52? (a) 85 (b) 8500 (c) 850
  27. 27.Best estimate of 382 ÷ 29? (a) 1300 (b) 13 (c) 130
  28. 28.√83 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 9.2 (d) 8.9
  29. 29.√78 to 1 decimal place? (a) 8.7 (b) 8.9 (c) 8.8 (d) 8.6
  30. 30.Best estimate of 2499 ÷ 64? (a) 4200 (b) 42 (c) 420
  31. 31.√27 to 1 decimal place? (a) 5.2 (b) 5.5 (c) 5.3 (d) 5.4
  32. 32.Best estimate of 888 ÷ 32? (a) 3000 (b) 300 (c) 30
  33. 33.Best estimate of 2490 ÷ 43? (a) 6200 (b) 620 (c) 62
  34. 34.√55 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.6 (d) 7.5
  35. 35.Best estimate of 1204 ÷ 37? (a) 30 (b) 300 (c) 3000
  36. 36.√59 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.8 (d) 7.7
  37. 37.√50 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 6.9 (d) 7.0
  38. 38.Best estimate of 3927 ÷ 66? (a) 5600 (b) 560 (c) 56
  39. 39.√70 to 1 decimal place? (a) 8.4 (b) 8.2 (c) 8.5 (d) 8.3
  40. 40.√90 to 1 decimal place? (a) 9.3 (b) 9.5 (c) 9.2 (d) 9.4

Answer key

  1. 7.1
  2. 5.8
  3. 60
  4. 4.9
  5. 13
  6. 48
  7. 23
  8. 7.3
  9. 24
  10. 62
  11. 61
  12. 32
  13. 8.1
  14. 6.2
  15. 17
  16. 93
  17. 6.1
  18. 61
  19. 7.2
  20. 6.4
  21. 8.1
  22. 11
  23. 8.2
  24. 75
  25. 54
  26. 85
  27. 13
  28. 9.1
  29. 8.8
  30. 42
  31. 5.2
  32. 30
  33. 62
  34. 7.4
  35. 30
  36. 7.7
  37. 7.1
  38. 56
  39. 8.4
  40. 9.5

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