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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 18 · 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.√48 to 1 decimal place? (a) 6.9 (b) 7.2 (c) 7.0 (d) 7.1
  2. 2.Best estimate of 3374 ÷ 77? (a) 4200 (b) 420 (c) 42
  3. 3.√53 to 1 decimal place? (a) 7.6 (b) 7.3 (c) 7.5 (d) 7.4
  4. 4.√37 to 1 decimal place? (a) 6.4 (b) 6.2 (c) 6.3 (d) 6.1
  5. 5.Best estimate of 3515 ÷ 59? (a) 5900 (b) 59 (c) 590
  6. 6.√45 to 1 decimal place? (a) 6.8 (b) 6.7 (c) 6.6 (d) 6.9
  7. 7.√34 to 1 decimal place? (a) 5.6 (b) 5.8 (c) 5.5 (d) 5.7
  8. 8.√83 to 1 decimal place? (a) 8.9 (b) 9.2 (c) 9.0 (d) 9.1
  9. 9.Best estimate of 3098 ÷ 56? (a) 52 (b) 5200 (c) 520
  10. 10.√87 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.1 (d) 9.2
  11. 11.√69 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 8.2 (d) 8.3
  12. 12.Best estimate of 2420 ÷ 88? (a) 2700 (b) 270 (c) 27
  13. 13.Best estimate of 3148 ÷ 52? (a) 6300 (b) 63 (c) 630
  14. 14.√76 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 9.0 (d) 8.7
  15. 15.√50 to 1 decimal place? (a) 7.4 (b) 7.1 (c) 7.3 (d) 7.2
  16. 16.Best estimate of 967 ÷ 38? (a) 2400 (b) 24 (c) 240
  17. 17.√35 to 1 decimal place? (a) 6.2 (b) 5.9 (c) 6.0 (d) 6.1
  18. 18.Best estimate of 5577 ÷ 66? (a) 800 (b) 8000 (c) 80
  19. 19.Best estimate of 1558 ÷ 86? (a) 17 (b) 1700 (c) 170
  20. 20.Best estimate of 1556 ÷ 52? (a) 310 (b) 3100 (c) 31
  21. 21.Best estimate of 5253 ÷ 73? (a) 750 (b) 7500 (c) 75
  22. 22.Best estimate of 3311 ÷ 62? (a) 5500 (b) 55 (c) 550
  23. 23.Best estimate of 5236 ÷ 69? (a) 750 (b) 75 (c) 7500
  24. 24.√92 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.7 (d) 9.6
  25. 25.√82 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.2 (d) 9.1
  26. 26.Best estimate of 2349 ÷ 51? (a) 47 (b) 470 (c) 4700
  27. 27.Best estimate of 1641 ÷ 51? (a) 3300 (b) 33 (c) 330
  28. 28.√31 to 1 decimal place? (a) 5.6 (b) 5.5 (c) 5.7 (d) 5.4
  29. 29.Best estimate of 620 ÷ 26? (a) 21 (b) 210 (c) 2100
  30. 30.√90 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.8 (d) 9.5
  31. 31.Best estimate of 545 ÷ 31? (a) 180 (b) 1800 (c) 18
  32. 32.√74 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.4 (d) 8.5
  33. 33.√44 to 1 decimal place? (a) 6.6 (b) 6.4 (c) 6.5 (d) 6.3
  34. 34.√46 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.5 (d) 6.8
  35. 35.√94 to 1 decimal place? (a) 10.0 (b) 9.9 (c) 9.8 (d) 9.7
  36. 36.Best estimate of 1856 ÷ 82? (a) 230 (b) 23 (c) 2300
  37. 37.Best estimate of 1025 ÷ 37? (a) 2600 (b) 26 (c) 260
  38. 38.Best estimate of 1682 ÷ 26? (a) 56 (b) 5600 (c) 560
  39. 39.Best estimate of 1478 ÷ 79? (a) 18 (b) 180 (c) 1800
  40. 40.Best estimate of 780 ÷ 46? (a) 160 (b) 1600 (c) 16

Answer key

  1. 6.9
  2. 42
  3. 7.3
  4. 6.1
  5. 59
  6. 6.7
  7. 5.8
  8. 9.1
  9. 52
  10. 9.3
  11. 8.3
  12. 27
  13. 63
  14. 8.7
  15. 7.1
  16. 24
  17. 5.9
  18. 80
  19. 17
  20. 31
  21. 75
  22. 55
  23. 75
  24. 9.6
  25. 9.1
  26. 47
  27. 33
  28. 5.6
  29. 21
  30. 9.5
  31. 18
  32. 8.6
  33. 6.6
  34. 6.8
  35. 9.7
  36. 23
  37. 26
  38. 56
  39. 18
  40. 16

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