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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 179 · 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 4308 ÷ 46? (a) 8600 (b) 860 (c) 86
  2. 2.√26 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.2 (d) 5.1
  3. 3.√63 to 1 decimal place? (a) 8.0 (b) 8.2 (c) 7.9 (d) 8.1
  4. 4.√31 to 1 decimal place? (a) 5.5 (b) 5.8 (c) 5.7 (d) 5.6
  5. 5.√98 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 10.0 (d) 9.7
  6. 6.Best estimate of 706 ÷ 56? (a) 120 (b) 12 (c) 1200
  7. 7.√74 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.6 (d) 8.5
  8. 8.Best estimate of 458 ÷ 26? (a) 150 (b) 15 (c) 1500
  9. 9.Best estimate of 1301 ÷ 26? (a) 43 (b) 430 (c) 4300
  10. 10.Best estimate of 902 ÷ 34? (a) 30 (b) 300 (c) 3000
  11. 11.√84 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 9.1 (d) 9.2
  12. 12.√43 to 1 decimal place? (a) 6.6 (b) 6.9 (c) 6.7 (d) 6.8
  13. 13.Best estimate of 3042 ÷ 56? (a) 51 (b) 510 (c) 5100
  14. 14.Best estimate of 2131 ÷ 82? (a) 270 (b) 2700 (c) 27
  15. 15.√42 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.7 (d) 6.4
  16. 16.Best estimate of 1529 ÷ 57? (a) 25 (b) 2500 (c) 250
  17. 17.Best estimate of 6014 ÷ 84? (a) 75 (b) 750 (c) 7500
  18. 18.√44 to 1 decimal place? (a) 6.4 (b) 6.6 (c) 6.5 (d) 6.3
  19. 19.Best estimate of 5960 ÷ 81? (a) 7500 (b) 75 (c) 750
  20. 20.Best estimate of 1724 ÷ 37? (a) 4300 (b) 43 (c) 430
  21. 21.√89 to 1 decimal place? (a) 9.7 (b) 9.4 (c) 9.5 (d) 9.6
  22. 22.Best estimate of 1860 ÷ 33? (a) 62 (b) 620 (c) 6200
  23. 23.Best estimate of 4217 ÷ 57? (a) 7000 (b) 700 (c) 70
  24. 24.√37 to 1 decimal place? (a) 6.0 (b) 5.9 (c) 6.1 (d) 5.8
  25. 25.Best estimate of 1918 ÷ 42? (a) 48 (b) 480 (c) 4800
  26. 26.√52 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 6.9 (d) 7.0
  27. 27.√23 to 1 decimal place? (a) 4.8 (b) 5.0 (c) 4.7 (d) 4.9
  28. 28.Best estimate of 1030 ÷ 68? (a) 150 (b) 1500 (c) 15
  29. 29.√80 to 1 decimal place? (a) 8.9 (b) 8.7 (c) 8.6 (d) 8.8
  30. 30.√96 to 1 decimal place? (a) 9.9 (b) 10.1 (c) 9.8 (d) 10.0
  31. 31.Best estimate of 2813 ÷ 81? (a) 350 (b) 3500 (c) 35
  32. 32.Best estimate of 641 ÷ 33? (a) 2100 (b) 21 (c) 210
  33. 33.Best estimate of 4296 ÷ 47? (a) 86 (b) 860 (c) 8600
  34. 34.√90 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.7 (d) 9.4
  35. 35.Best estimate of 3058 ÷ 36? (a) 76 (b) 760 (c) 7600
  36. 36.Best estimate of 1617 ÷ 24? (a) 8100 (b) 81 (c) 810
  37. 37.√40 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.4 (d) 6.3
  38. 38.√29 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.4 (d) 5.5
  39. 39.Best estimate of 1803 ÷ 52? (a) 360 (b) 3600 (c) 36
  40. 40.√51 to 1 decimal place? (a) 7.1 (b) 7.4 (c) 7.3 (d) 7.2

Answer key

  1. 86
  2. 5.1
  3. 7.9
  4. 5.6
  5. 9.9
  6. 12
  7. 8.6
  8. 15
  9. 43
  10. 30
  11. 9.2
  12. 6.6
  13. 51
  14. 27
  15. 6.5
  16. 25
  17. 75
  18. 6.6
  19. 75
  20. 43
  21. 9.4
  22. 62
  23. 70
  24. 6.1
  25. 48
  26. 7.2
  27. 4.8
  28. 15
  29. 8.9
  30. 9.8
  31. 35
  32. 21
  33. 86
  34. 9.5
  35. 76
  36. 81
  37. 6.3
  38. 5.4
  39. 36
  40. 7.1

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