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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 329 · 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 2603 ÷ 43? (a) 650 (b) 6500 (c) 65
  2. 2.Best estimate of 4718 ÷ 58? (a) 79 (b) 7900 (c) 790
  3. 3.Best estimate of 3315 ÷ 62? (a) 55 (b) 5500 (c) 550
  4. 4.√37 to 1 decimal place? (a) 5.9 (b) 6.1 (c) 6.2 (d) 6.0
  5. 5.Best estimate of 4572 ÷ 62? (a) 7600 (b) 760 (c) 76
  6. 6.Best estimate of 1543 ÷ 47? (a) 31 (b) 3100 (c) 310
  7. 7.√56 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.7 (d) 7.6
  8. 8.Best estimate of 975 ÷ 42? (a) 24 (b) 240 (c) 2400
  9. 9.√74 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.9 (d) 8.6
  10. 10.√45 to 1 decimal place? (a) 6.5 (b) 6.7 (c) 6.4 (d) 6.6
  11. 11.√58 to 1 decimal place? (a) 7.6 (b) 7.4 (c) 7.3 (d) 7.5
  12. 12.Best estimate of 310 ÷ 24? (a) 1600 (b) 16 (c) 160
  13. 13.√40 to 1 decimal place? (a) 6.4 (b) 6.2 (c) 6.5 (d) 6.3
  14. 14.Best estimate of 2613 ÷ 41? (a) 6500 (b) 65 (c) 650
  15. 15.Best estimate of 1477 ÷ 73? (a) 210 (b) 21 (c) 2100
  16. 16.√20 to 1 decimal place? (a) 4.3 (b) 4.4 (c) 4.6 (d) 4.5
  17. 17.Best estimate of 3954 ÷ 73? (a) 56 (b) 560 (c) 5600
  18. 18.√55 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.2 (d) 7.3
  19. 19.√85 to 1 decimal place? (a) 8.9 (b) 9.1 (c) 9.2 (d) 9.0
  20. 20.√34 to 1 decimal place? (a) 5.8 (b) 5.6 (c) 5.7 (d) 5.5
  21. 21.√83 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.0 (d) 9.1
  22. 22.Best estimate of 5114 ÷ 56? (a) 850 (b) 8500 (c) 85
  23. 23.Best estimate of 5796 ÷ 62? (a) 9700 (b) 97 (c) 970
  24. 24.Best estimate of 6204 ÷ 84? (a) 780 (b) 7800 (c) 78
  25. 25.Best estimate of 840 ÷ 24? (a) 420 (b) 42 (c) 4200
  26. 26.Best estimate of 3584 ÷ 88? (a) 4000 (b) 400 (c) 40
  27. 27.√96 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.8 (d) 9.5
  28. 28.Best estimate of 2677 ÷ 34? (a) 890 (b) 89 (c) 8900
  29. 29.√94 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.8 (d) 9.9
  30. 30.√29 to 1 decimal place? (a) 5.5 (b) 5.2 (c) 5.4 (d) 5.3
  31. 31.Best estimate of 1803 ÷ 22? (a) 9000 (b) 90 (c) 900
  32. 32.Best estimate of 488 ÷ 37? (a) 12 (b) 1200 (c) 120
  33. 33.Best estimate of 3199 ÷ 47? (a) 64 (b) 6400 (c) 640
  34. 34.√98 to 1 decimal place? (a) 10.1 (b) 10.0 (c) 10.2 (d) 9.9
  35. 35.√65 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 8.0 (d) 8.1
  36. 36.√38 to 1 decimal place? (a) 6.5 (b) 6.3 (c) 6.4 (d) 6.2
  37. 37.Best estimate of 2786 ÷ 66? (a) 4000 (b) 400 (c) 40
  38. 38.√69 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.6 (d) 8.3
  39. 39.Best estimate of 3070 ÷ 49? (a) 6100 (b) 610 (c) 61
  40. 40.Best estimate of 1540 ÷ 61? (a) 260 (b) 26 (c) 2600

Answer key

  1. 65
  2. 79
  3. 55
  4. 6.1
  5. 76
  6. 31
  7. 7.5
  8. 24
  9. 8.6
  10. 6.7
  11. 7.6
  12. 16
  13. 6.3
  14. 65
  15. 21
  16. 4.5
  17. 56
  18. 7.4
  19. 9.2
  20. 5.8
  21. 9.1
  22. 85
  23. 97
  24. 78
  25. 42
  26. 40
  27. 9.8
  28. 89
  29. 9.7
  30. 5.4
  31. 90
  32. 12
  33. 64
  34. 9.9
  35. 8.1
  36. 6.2
  37. 40
  38. 8.3
  39. 61
  40. 26

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