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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 157 · 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 2519 ÷ 39? (a) 6300 (b) 630 (c) 63
  2. 2.Best estimate of 1592 ÷ 76? (a) 2000 (b) 20 (c) 200
  3. 3.√59 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 7.7 (d) 8.0
  4. 4.Best estimate of 3810 ÷ 62? (a) 64 (b) 640 (c) 6400
  5. 5.√96 to 1 decimal place? (a) 9.6 (b) 9.8 (c) 9.5 (d) 9.7
  6. 6.√55 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.4 (d) 7.7
  7. 7.√27 to 1 decimal place? (a) 5.2 (b) 4.9 (c) 5.1 (d) 5.0
  8. 8.√61 to 1 decimal place? (a) 7.7 (b) 7.9 (c) 7.8 (d) 8.0
  9. 9.Best estimate of 4833 ÷ 62? (a) 81 (b) 810 (c) 8100
  10. 10.√22 to 1 decimal place? (a) 4.8 (b) 4.5 (c) 4.7 (d) 4.6
  11. 11.Best estimate of 4251 ÷ 66? (a) 610 (b) 6100 (c) 61
  12. 12.Best estimate of 919 ÷ 76? (a) 11 (b) 1100 (c) 110
  13. 13.√34 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 5.6 (d) 5.7
  14. 14.√41 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.6 (d) 6.5
  15. 15.Best estimate of 1022 ÷ 29? (a) 340 (b) 34 (c) 3400
  16. 16.Best estimate of 877 ÷ 33? (a) 29 (b) 2900 (c) 290
  17. 17.Best estimate of 2507 ÷ 36? (a) 630 (b) 6300 (c) 63
  18. 18.Best estimate of 1344 ÷ 29? (a) 4500 (b) 45 (c) 450
  19. 19.Best estimate of 5088 ÷ 69? (a) 7300 (b) 730 (c) 73
  20. 20.Best estimate of 2841 ÷ 48? (a) 5700 (b) 570 (c) 57
  21. 21.Best estimate of 5372 ÷ 84? (a) 67 (b) 6700 (c) 670
  22. 22.Best estimate of 2322 ÷ 59? (a) 39 (b) 3900 (c) 390
  23. 23.Best estimate of 2051 ÷ 39? (a) 510 (b) 51 (c) 5100
  24. 24.Best estimate of 2925 ÷ 44? (a) 730 (b) 7300 (c) 73
  25. 25.Best estimate of 2537 ÷ 51? (a) 510 (b) 5100 (c) 51
  26. 26.√70 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.4 (d) 8.1
  27. 27.Best estimate of 834 ÷ 26? (a) 280 (b) 2800 (c) 28
  28. 28.Best estimate of 1461 ÷ 34? (a) 490 (b) 4900 (c) 49
  29. 29.Best estimate of 2590 ÷ 86? (a) 29 (b) 2900 (c) 290
  30. 30.√58 to 1 decimal place? (a) 7.8 (b) 7.6 (c) 7.7 (d) 7.5
  31. 31.√37 to 1 decimal place? (a) 6.0 (b) 5.9 (c) 6.1 (d) 6.2
  32. 32.Best estimate of 2544 ÷ 42? (a) 640 (b) 6400 (c) 64
  33. 33.√69 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.5 (d) 8.2
  34. 34.Best estimate of 4373 ÷ 46? (a) 87 (b) 870 (c) 8700
  35. 35.Best estimate of 997 ÷ 32? (a) 3300 (b) 330 (c) 33
  36. 36.Best estimate of 1729 ÷ 66? (a) 2500 (b) 25 (c) 250
  37. 37.√94 to 1 decimal place? (a) 9.8 (b) 9.5 (c) 9.7 (d) 9.6
  38. 38.Best estimate of 3710 ÷ 56? (a) 620 (b) 6200 (c) 62
  39. 39.√75 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.7 (d) 9.0
  40. 40.√35 to 1 decimal place? (a) 6.0 (b) 6.2 (c) 5.9 (d) 6.1

Answer key

  1. 63
  2. 20
  3. 7.7
  4. 64
  5. 9.8
  6. 7.4
  7. 5.2
  8. 7.8
  9. 81
  10. 4.7
  11. 61
  12. 11
  13. 5.8
  14. 6.4
  15. 34
  16. 29
  17. 63
  18. 45
  19. 73
  20. 57
  21. 67
  22. 39
  23. 51
  24. 73
  25. 51
  26. 8.4
  27. 28
  28. 49
  29. 29
  30. 7.6
  31. 6.1
  32. 64
  33. 8.3
  34. 87
  35. 33
  36. 25
  37. 9.7
  38. 62
  39. 8.7
  40. 5.9

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