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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 860 · 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.√61 to 1 decimal place? (a) 7.6 (b) 7.7 (c) 7.5 (d) 7.8
  2. 2.Best estimate of 1804 ÷ 29? (a) 600 (b) 6000 (c) 60
  3. 3.√78 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.7 (d) 8.5
  4. 4.√58 to 1 decimal place? (a) 7.4 (b) 7.6 (c) 7.3 (d) 7.5
  5. 5.√59 to 1 decimal place? (a) 7.8 (b) 7.5 (c) 7.7 (d) 7.6
  6. 6.√35 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.8 (d) 5.9
  7. 7.√53 to 1 decimal place? (a) 7.3 (b) 7.5 (c) 7.4 (d) 7.2
  8. 8.√74 to 1 decimal place? (a) 8.8 (b) 8.7 (c) 8.6 (d) 8.5
  9. 9.Best estimate of 3179 ÷ 34? (a) 1060 (b) 106 (c) 10600
  10. 10.Best estimate of 1162 ÷ 36? (a) 290 (b) 29 (c) 2900
  11. 11.Best estimate of 1023 ÷ 32? (a) 340 (b) 3400 (c) 34
  12. 12.Best estimate of 3209 ÷ 53? (a) 6400 (b) 640 (c) 64
  13. 13.√47 to 1 decimal place? (a) 6.8 (b) 6.7 (c) 6.6 (d) 6.9
  14. 14.Best estimate of 2134 ÷ 38? (a) 5300 (b) 53 (c) 530
  15. 15.Best estimate of 650 ÷ 26? (a) 220 (b) 2200 (c) 22
  16. 16.√70 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.4 (d) 8.1
  17. 17.Best estimate of 3740 ÷ 49? (a) 750 (b) 75 (c) 7500
  18. 18.Best estimate of 3447 ÷ 83? (a) 4300 (b) 43 (c) 430
  19. 19.Best estimate of 5451 ÷ 79? (a) 6800 (b) 680 (c) 68
  20. 20.√69 to 1 decimal place? (a) 8.1 (b) 8.3 (c) 8.2 (d) 8.4
  21. 21.√21 to 1 decimal place? (a) 4.4 (b) 4.3 (c) 4.6 (d) 4.5
  22. 22.Best estimate of 2481 ÷ 37? (a) 62 (b) 6200 (c) 620
  23. 23.√40 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.2 (d) 6.1
  24. 24.Best estimate of 2953 ÷ 51? (a) 590 (b) 5900 (c) 59
  25. 25.Best estimate of 1315 ÷ 76? (a) 1600 (b) 160 (c) 16
  26. 26.√88 to 1 decimal place? (a) 9.3 (b) 9.5 (c) 9.2 (d) 9.4
  27. 27.Best estimate of 3208 ÷ 66? (a) 46 (b) 4600 (c) 460
  28. 28.√92 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.6 (d) 9.3
  29. 29.√37 to 1 decimal place? (a) 5.9 (b) 6.0 (c) 6.1 (d) 5.8
  30. 30.√41 to 1 decimal place? (a) 6.1 (b) 6.2 (c) 6.4 (d) 6.3
  31. 31.√30 to 1 decimal place? (a) 5.3 (b) 5.5 (c) 5.4 (d) 5.2
  32. 32.√98 to 1 decimal place? (a) 9.9 (b) 10.0 (c) 10.1 (d) 10.2
  33. 33.Best estimate of 2187 ÷ 61? (a) 360 (b) 3600 (c) 36
  34. 34.√20 to 1 decimal place? (a) 4.4 (b) 4.3 (c) 4.6 (d) 4.5
  35. 35.Best estimate of 3584 ÷ 84? (a) 4500 (b) 450 (c) 45
  36. 36.Best estimate of 748 ÷ 33? (a) 250 (b) 25 (c) 2500
  37. 37.√42 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.7 (d) 6.6
  38. 38.Best estimate of 3762 ÷ 78? (a) 47 (b) 470 (c) 4700
  39. 39.√77 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 8.6 (d) 8.7
  40. 40.√96 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.8 (d) 9.7

Answer key

  1. 7.8
  2. 60
  3. 8.8
  4. 7.6
  5. 7.7
  6. 5.9
  7. 7.3
  8. 8.6
  9. 106
  10. 29
  11. 34
  12. 64
  13. 6.9
  14. 53
  15. 22
  16. 8.4
  17. 75
  18. 43
  19. 68
  20. 8.3
  21. 4.6
  22. 62
  23. 6.3
  24. 59
  25. 16
  26. 9.4
  27. 46
  28. 9.6
  29. 6.1
  30. 6.4
  31. 5.5
  32. 9.9
  33. 36
  34. 4.5
  35. 45
  36. 25
  37. 6.5
  38. 47
  39. 8.8
  40. 9.8

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