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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 279 · 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.Best estimate of 2745 ÷ 42? (a) 690 (b) 6900 (c) 69
  2. 2.Best estimate of 4399 ÷ 47? (a) 8800 (b) 88 (c) 880
  3. 3.√94 to 1 decimal place? (a) 9.4 (b) 9.6 (c) 9.7 (d) 9.5
  4. 4.√61 to 1 decimal place? (a) 8.0 (b) 7.9 (c) 8.1 (d) 7.8
  5. 5.√72 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.4 (d) 8.7
  6. 6.Best estimate of 1316 ÷ 22? (a) 660 (b) 6600 (c) 66
  7. 7.√34 to 1 decimal place? (a) 6.0 (b) 5.7 (c) 5.9 (d) 5.8
  8. 8.Best estimate of 1115 ÷ 24? (a) 5600 (b) 56 (c) 560
  9. 9.√50 to 1 decimal place? (a) 6.9 (b) 7.1 (c) 7.0 (d) 6.8
  10. 10.Best estimate of 4237 ÷ 64? (a) 710 (b) 7100 (c) 71
  11. 11.Best estimate of 609 ÷ 23? (a) 300 (b) 3000 (c) 30
  12. 12.Best estimate of 455 ÷ 28? (a) 150 (b) 15 (c) 1500
  13. 13.√22 to 1 decimal place? (a) 4.6 (b) 4.7 (c) 4.8 (d) 4.9
  14. 14.Best estimate of 815 ÷ 38? (a) 200 (b) 2000 (c) 20
  15. 15.√20 to 1 decimal place? (a) 4.4 (b) 4.3 (c) 4.5 (d) 4.2
  16. 16.Best estimate of 2651 ÷ 33? (a) 8800 (b) 880 (c) 88
  17. 17.Best estimate of 2390 ÷ 87? (a) 27 (b) 2700 (c) 270
  18. 18.√82 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.1 (d) 9.2
  19. 19.Best estimate of 1844 ÷ 29? (a) 61 (b) 610 (c) 6100
  20. 20.√43 to 1 decimal place? (a) 6.5 (b) 6.7 (c) 6.4 (d) 6.6
  21. 21.√71 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.6 (d) 8.7
  22. 22.Best estimate of 1511 ÷ 32? (a) 5000 (b) 50 (c) 500
  23. 23.√40 to 1 decimal place? (a) 6.4 (b) 6.1 (c) 6.2 (d) 6.3
  24. 24.√28 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.6 (d) 5.5
  25. 25.√56 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.4 (d) 7.7
  26. 26.√63 to 1 decimal place? (a) 7.8 (b) 8.0 (c) 7.9 (d) 8.1
  27. 27.√51 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 7.0 (d) 6.9
  28. 28.Best estimate of 3264 ÷ 54? (a) 6500 (b) 650 (c) 65
  29. 29.Best estimate of 5747 ÷ 86? (a) 6400 (b) 640 (c) 64
  30. 30.Best estimate of 1555 ÷ 48? (a) 310 (b) 3100 (c) 31
  31. 31.Best estimate of 4721 ÷ 72? (a) 670 (b) 6700 (c) 67
  32. 32.Best estimate of 5196 ÷ 79? (a) 650 (b) 6500 (c) 65
  33. 33.√66 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.4 (d) 8.3
  34. 34.√27 to 1 decimal place? (a) 5.2 (b) 5.5 (c) 5.4 (d) 5.3
  35. 35.Best estimate of 3557 ÷ 69? (a) 510 (b) 51 (c) 5100
  36. 36.√35 to 1 decimal place? (a) 5.8 (b) 6.0 (c) 5.9 (d) 5.7
  37. 37.Best estimate of 2032 ÷ 49? (a) 4100 (b) 41 (c) 410
  38. 38.Best estimate of 2260 ÷ 82? (a) 28 (b) 2800 (c) 280
  39. 39.Best estimate of 1474 ÷ 42? (a) 37 (b) 370 (c) 3700
  40. 40.√26 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.0 (d) 5.1

Answer key

  1. 69
  2. 88
  3. 9.7
  4. 7.8
  5. 8.5
  6. 66
  7. 5.8
  8. 56
  9. 7.1
  10. 71
  11. 30
  12. 15
  13. 4.7
  14. 20
  15. 4.5
  16. 88
  17. 27
  18. 9.1
  19. 61
  20. 6.6
  21. 8.4
  22. 50
  23. 6.3
  24. 5.3
  25. 7.5
  26. 7.9
  27. 7.1
  28. 65
  29. 64
  30. 31
  31. 67
  32. 65
  33. 8.1
  34. 5.2
  35. 51
  36. 5.9
  37. 41
  38. 28
  39. 37
  40. 5.1

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