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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 600 · 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.√55 to 1 decimal place? (a) 7.4 (b) 7.6 (c) 7.3 (d) 7.5
  2. 2.Best estimate of 1351 ÷ 24? (a) 6800 (b) 68 (c) 680
  3. 3.√27 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.5 (d) 5.4
  4. 4.√58 to 1 decimal place? (a) 7.6 (b) 7.4 (c) 7.7 (d) 7.5
  5. 5.Best estimate of 884 ÷ 22? (a) 44 (b) 4400 (c) 440
  6. 6.√96 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.8 (d) 9.5
  7. 7.Best estimate of 3843 ÷ 78? (a) 48 (b) 480 (c) 4800
  8. 8.Best estimate of 4926 ÷ 72? (a) 7000 (b) 70 (c) 700
  9. 9.Best estimate of 1459 ÷ 58? (a) 24 (b) 240 (c) 2400
  10. 10.√86 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.4 (d) 9.1
  11. 11.√92 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.4 (d) 9.7
  12. 12.Best estimate of 5426 ÷ 66? (a) 780 (b) 78 (c) 7800
  13. 13.√44 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.7 (d) 6.4
  14. 14.Best estimate of 4241 ÷ 71? (a) 6100 (b) 61 (c) 610
  15. 15.Best estimate of 1230 ÷ 68? (a) 1800 (b) 18 (c) 180
  16. 16.√75 to 1 decimal place? (a) 8.4 (b) 8.7 (c) 8.6 (d) 8.5
  17. 17.Best estimate of 1591 ÷ 31? (a) 53 (b) 5300 (c) 530
  18. 18.Best estimate of 3443 ÷ 84? (a) 430 (b) 43 (c) 4300
  19. 19.√41 to 1 decimal place? (a) 6.6 (b) 6.4 (c) 6.5 (d) 6.7
  20. 20.Best estimate of 4407 ÷ 72? (a) 630 (b) 6300 (c) 63
  21. 21.√32 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.7 (d) 5.6
  22. 22.√28 to 1 decimal place? (a) 5.4 (b) 5.5 (c) 5.3 (d) 5.6
  23. 23.Best estimate of 1021 ÷ 42? (a) 260 (b) 2600 (c) 26
  24. 24.Best estimate of 2239 ÷ 62? (a) 37 (b) 3700 (c) 370
  25. 25.Best estimate of 4866 ÷ 84? (a) 61 (b) 6100 (c) 610
  26. 26.Best estimate of 6239 ÷ 83? (a) 7800 (b) 780 (c) 78
  27. 27.√90 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.3 (d) 9.6
  28. 28.√23 to 1 decimal place? (a) 4.7 (b) 4.6 (c) 4.9 (d) 4.8
  29. 29.√61 to 1 decimal place? (a) 7.9 (b) 8.1 (c) 7.8 (d) 8.0
  30. 30.Best estimate of 2707 ÷ 78? (a) 34 (b) 340 (c) 3400
  31. 31.√26 to 1 decimal place? (a) 5.0 (b) 4.9 (c) 5.1 (d) 4.8
  32. 32.Best estimate of 5524 ÷ 81? (a) 69 (b) 690 (c) 6900
  33. 33.√34 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.6 (d) 5.5
  34. 34.Best estimate of 4354 ÷ 72? (a) 6200 (b) 620 (c) 62
  35. 35.Best estimate of 2103 ÷ 67? (a) 30 (b) 300 (c) 3000
  36. 36.Best estimate of 4095 ÷ 46? (a) 820 (b) 82 (c) 8200
  37. 37.Best estimate of 1464 ÷ 24? (a) 7300 (b) 73 (c) 730
  38. 38.Best estimate of 1922 ÷ 26? (a) 6400 (b) 64 (c) 640
  39. 39.Best estimate of 2786 ÷ 52? (a) 56 (b) 560 (c) 5600
  40. 40.Best estimate of 2019 ÷ 27? (a) 6700 (b) 670 (c) 67

Answer key

  1. 7.4
  2. 68
  3. 5.2
  4. 7.6
  5. 44
  6. 9.8
  7. 48
  8. 70
  9. 24
  10. 9.3
  11. 9.6
  12. 78
  13. 6.6
  14. 61
  15. 18
  16. 8.7
  17. 53
  18. 43
  19. 6.4
  20. 63
  21. 5.7
  22. 5.3
  23. 26
  24. 37
  25. 61
  26. 78
  27. 9.5
  28. 4.8
  29. 7.8
  30. 34
  31. 5.1
  32. 69
  33. 5.8
  34. 62
  35. 30
  36. 82
  37. 73
  38. 64
  39. 56
  40. 67

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