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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 444 · 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) 7.3 (d) 7.1
  2. 2.√70 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.4 (d) 8.5
  3. 3.√82 to 1 decimal place? (a) 9.0 (b) 8.8 (c) 8.9 (d) 9.1
  4. 4.Best estimate of 3097 ÷ 77? (a) 390 (b) 3900 (c) 39
  5. 5.√26 to 1 decimal place? (a) 5.1 (b) 5.4 (c) 5.2 (d) 5.3
  6. 6.Best estimate of 7708 ÷ 86? (a) 860 (b) 8600 (c) 86
  7. 7.√65 to 1 decimal place? (a) 8.1 (b) 8.3 (c) 8.2 (d) 8.0
  8. 8.Best estimate of 1285 ÷ 36? (a) 3200 (b) 320 (c) 32
  9. 9.Best estimate of 1009 ÷ 33? (a) 3400 (b) 34 (c) 340
  10. 10.√66 to 1 decimal place? (a) 8.2 (b) 8.4 (c) 8.1 (d) 8.3
  11. 11.√62 to 1 decimal place? (a) 7.9 (b) 8.1 (c) 8.2 (d) 8.0
  12. 12.Best estimate of 2152 ÷ 81? (a) 2700 (b) 270 (c) 27
  13. 13.√74 to 1 decimal place? (a) 8.8 (b) 8.5 (c) 8.7 (d) 8.6
  14. 14.Best estimate of 2021 ÷ 56? (a) 34 (b) 340 (c) 3400
  15. 15.Best estimate of 1633 ÷ 42? (a) 410 (b) 41 (c) 4100
  16. 16.√28 to 1 decimal place? (a) 5.2 (b) 5.1 (c) 5.0 (d) 5.3
  17. 17.√34 to 1 decimal place? (a) 6.0 (b) 6.1 (c) 5.9 (d) 5.8
  18. 18.√22 to 1 decimal place? (a) 4.4 (b) 4.7 (c) 4.5 (d) 4.6
  19. 19.Best estimate of 4896 ÷ 52? (a) 980 (b) 9800 (c) 98
  20. 20.Best estimate of 3997 ÷ 66? (a) 57 (b) 5700 (c) 570
  21. 21.Best estimate of 1366 ÷ 36? (a) 340 (b) 3400 (c) 34
  22. 22.√21 to 1 decimal place? (a) 4.5 (b) 4.4 (c) 4.6 (d) 4.3
  23. 23.√29 to 1 decimal place? (a) 5.3 (b) 5.5 (c) 5.4 (d) 5.6
  24. 24.√75 to 1 decimal place? (a) 8.6 (b) 8.4 (c) 8.5 (d) 8.7
  25. 25.√38 to 1 decimal place? (a) 6.4 (b) 6.2 (c) 6.3 (d) 6.1
  26. 26.Best estimate of 1206 ÷ 42? (a) 3000 (b) 30 (c) 300
  27. 27.Best estimate of 3729 ÷ 74? (a) 530 (b) 5300 (c) 53
  28. 28.√44 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.4 (d) 6.5
  29. 29.Best estimate of 1961 ÷ 37? (a) 4900 (b) 49 (c) 490
  30. 30.√40 to 1 decimal place? (a) 6.4 (b) 6.6 (c) 6.3 (d) 6.5
  31. 31.Best estimate of 2140 ÷ 72? (a) 31 (b) 310 (c) 3100
  32. 32.Best estimate of 1419 ÷ 29? (a) 47 (b) 4700 (c) 470
  33. 33.Best estimate of 3534 ÷ 48? (a) 710 (b) 7100 (c) 71
  34. 34.Best estimate of 1772 ÷ 24? (a) 89 (b) 8900 (c) 890
  35. 35.Best estimate of 1659 ÷ 26? (a) 550 (b) 55 (c) 5500
  36. 36.Best estimate of 3117 ÷ 73? (a) 450 (b) 4500 (c) 45
  37. 37.Best estimate of 4466 ÷ 57? (a) 74 (b) 740 (c) 7400
  38. 38.Best estimate of 5297 ÷ 69? (a) 760 (b) 7600 (c) 76
  39. 39.Best estimate of 3442 ÷ 51? (a) 69 (b) 6900 (c) 690
  40. 40.√98 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 10.0 (d) 9.8

Answer key

  1. 7.4
  2. 8.4
  3. 9.1
  4. 39
  5. 5.1
  6. 86
  7. 8.1
  8. 32
  9. 34
  10. 8.1
  11. 7.9
  12. 27
  13. 8.6
  14. 34
  15. 41
  16. 5.3
  17. 5.8
  18. 4.7
  19. 98
  20. 57
  21. 34
  22. 4.6
  23. 5.4
  24. 8.7
  25. 6.2
  26. 30
  27. 53
  28. 6.6
  29. 49
  30. 6.3
  31. 31
  32. 47
  33. 71
  34. 89
  35. 55
  36. 45
  37. 74
  38. 76
  39. 69
  40. 9.9

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