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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 325 · 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) 7.2 (c) 7.1 (d) 7.3
  2. 2.Best estimate of 6716 ÷ 88? (a) 75 (b) 750 (c) 7500
  3. 3.√32 to 1 decimal place? (a) 5.5 (b) 5.6 (c) 5.4 (d) 5.7
  4. 4.√53 to 1 decimal place? (a) 7.3 (b) 7.2 (c) 7.0 (d) 7.1
  5. 5.√61 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.8 (d) 7.7
  6. 6.√98 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 9.6 (d) 9.8
  7. 7.√21 to 1 decimal place? (a) 4.8 (b) 4.5 (c) 4.7 (d) 4.6
  8. 8.√78 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 8.8 (d) 9.1
  9. 9.Best estimate of 3163 ÷ 49? (a) 630 (b) 6300 (c) 63
  10. 10.√34 to 1 decimal place? (a) 6.1 (b) 5.8 (c) 6.0 (d) 5.9
  11. 11.√65 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.1 (d) 8.2
  12. 12.Best estimate of 3620 ÷ 52? (a) 720 (b) 72 (c) 7200
  13. 13.Best estimate of 895 ÷ 43? (a) 220 (b) 2200 (c) 22
  14. 14.Best estimate of 1747 ÷ 57? (a) 2900 (b) 290 (c) 29
  15. 15.√58 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.7 (d) 7.8
  16. 16.Best estimate of 4032 ÷ 66? (a) 58 (b) 5800 (c) 580
  17. 17.√90 to 1 decimal place? (a) 9.5 (b) 9.3 (c) 9.6 (d) 9.4
  18. 18.Best estimate of 5057 ÷ 67? (a) 720 (b) 72 (c) 7200
  19. 19.√23 to 1 decimal place? (a) 4.9 (b) 4.7 (c) 5.0 (d) 4.8
  20. 20.Best estimate of 5308 ÷ 78? (a) 660 (b) 66 (c) 6600
  21. 21.√22 to 1 decimal place? (a) 4.9 (b) 5.0 (c) 4.8 (d) 4.7
  22. 22.Best estimate of 1607 ÷ 26? (a) 5400 (b) 540 (c) 54
  23. 23.√37 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.1 (d) 6.3
  24. 24.√47 to 1 decimal place? (a) 6.9 (b) 7.2 (c) 7.1 (d) 7.0
  25. 25.Best estimate of 3606 ÷ 56? (a) 600 (b) 6000 (c) 60
  26. 26.Best estimate of 3804 ÷ 51? (a) 760 (b) 7600 (c) 76
  27. 27.√51 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 7.0 (d) 7.1
  28. 28.Best estimate of 1014 ÷ 28? (a) 340 (b) 3400 (c) 34
  29. 29.√38 to 1 decimal place? (a) 5.9 (b) 6.1 (c) 6.0 (d) 6.2
  30. 30.√40 to 1 decimal place? (a) 6.4 (b) 6.1 (c) 6.3 (d) 6.2
  31. 31.Best estimate of 4436 ÷ 67? (a) 63 (b) 6300 (c) 630
  32. 32.Best estimate of 4661 ÷ 62? (a) 78 (b) 7800 (c) 780
  33. 33.Best estimate of 3516 ÷ 61? (a) 59 (b) 590 (c) 5900
  34. 34.Best estimate of 930 ÷ 77? (a) 120 (b) 1200 (c) 12
  35. 35.Best estimate of 1327 ÷ 63? (a) 2200 (b) 220 (c) 22
  36. 36.√31 to 1 decimal place? (a) 5.8 (b) 5.5 (c) 5.6 (d) 5.7
  37. 37.√56 to 1 decimal place? (a) 7.3 (b) 7.6 (c) 7.5 (d) 7.4
  38. 38.√42 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.4 (d) 6.5
  39. 39.Best estimate of 1476 ÷ 23? (a) 7400 (b) 74 (c) 740
  40. 40.Best estimate of 4409 ÷ 51? (a) 8800 (b) 880 (c) 88

Answer key

  1. 7.4
  2. 75
  3. 5.7
  4. 7.3
  5. 7.8
  6. 9.9
  7. 4.6
  8. 8.8
  9. 63
  10. 5.8
  11. 8.1
  12. 72
  13. 22
  14. 29
  15. 7.6
  16. 58
  17. 9.5
  18. 72
  19. 4.8
  20. 66
  21. 4.7
  22. 54
  23. 6.1
  24. 6.9
  25. 60
  26. 76
  27. 7.1
  28. 34
  29. 6.2
  30. 6.3
  31. 63
  32. 78
  33. 59
  34. 12
  35. 22
  36. 5.6
  37. 7.5
  38. 6.5
  39. 74
  40. 88

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