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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 844 · 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.√79 to 1 decimal place? (a) 9.0 (b) 9.2 (c) 9.1 (d) 8.9
  2. 2.√59 to 1 decimal place? (a) 7.7 (b) 7.5 (c) 7.6 (d) 7.8
  3. 3.Best estimate of 1924 ÷ 67? (a) 2700 (b) 270 (c) 27
  4. 4.Best estimate of 2940 ÷ 36? (a) 7400 (b) 740 (c) 74
  5. 5.√72 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.4 (d) 8.7
  6. 6.Best estimate of 1436 ÷ 41? (a) 360 (b) 3600 (c) 36
  7. 7.Best estimate of 6137 ÷ 89? (a) 68 (b) 680 (c) 6800
  8. 8.√22 to 1 decimal place? (a) 4.7 (b) 4.6 (c) 4.8 (d) 4.5
  9. 9.Best estimate of 1580 ÷ 51? (a) 32 (b) 3200 (c) 320
  10. 10.Best estimate of 964 ÷ 42? (a) 2400 (b) 24 (c) 240
  11. 11.√61 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 7.9 (d) 8.0
  12. 12.Best estimate of 6004 ÷ 74? (a) 8600 (b) 86 (c) 860
  13. 13.√35 to 1 decimal place? (a) 6.0 (b) 6.2 (c) 5.9 (d) 6.1
  14. 14.√50 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 6.9 (d) 7.0
  15. 15.Best estimate of 2052 ÷ 73? (a) 29 (b) 290 (c) 2900
  16. 16.√82 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 9.2 (d) 8.9
  17. 17.√31 to 1 decimal place? (a) 5.7 (b) 5.9 (c) 5.6 (d) 5.8
  18. 18.Best estimate of 2240 ÷ 37? (a) 56 (b) 5600 (c) 560
  19. 19.√65 to 1 decimal place? (a) 8.1 (b) 8.3 (c) 8.0 (d) 8.2
  20. 20.√20 to 1 decimal place? (a) 4.5 (b) 4.4 (c) 4.6 (d) 4.3
  21. 21.Best estimate of 3685 ÷ 39? (a) 9200 (b) 920 (c) 92
  22. 22.Best estimate of 1341 ÷ 37? (a) 340 (b) 34 (c) 3400
  23. 23.Best estimate of 5579 ÷ 62? (a) 930 (b) 9300 (c) 93
  24. 24.Best estimate of 2488 ÷ 36? (a) 62 (b) 620 (c) 6200
  25. 25.Best estimate of 2462 ÷ 26? (a) 8200 (b) 82 (c) 820
  26. 26.Best estimate of 1085 ÷ 41? (a) 27 (b) 270 (c) 2700
  27. 27.Best estimate of 993 ÷ 38? (a) 2500 (b) 25 (c) 250
  28. 28.√83 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 9.3 (d) 9.4
  29. 29.Best estimate of 3497 ÷ 53? (a) 70 (b) 7000 (c) 700
  30. 30.√23 to 1 decimal place? (a) 4.7 (b) 4.9 (c) 4.8 (d) 5.0
  31. 31.Best estimate of 4477 ÷ 89? (a) 50 (b) 500 (c) 5000
  32. 32.Best estimate of 1458 ÷ 29? (a) 490 (b) 4900 (c) 49
  33. 33.Best estimate of 4946 ÷ 56? (a) 820 (b) 8200 (c) 82
  34. 34.√75 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.7 (d) 8.4
  35. 35.√69 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.3 (d) 8.4
  36. 36.√70 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.1 (d) 8.2
  37. 37.Best estimate of 2412 ÷ 28? (a) 800 (b) 8000 (c) 80
  38. 38.Best estimate of 5661 ÷ 76? (a) 71 (b) 7100 (c) 710
  39. 39.Best estimate of 3136 ÷ 52? (a) 6300 (b) 630 (c) 63
  40. 40.Best estimate of 3662 ÷ 56? (a) 6100 (b) 61 (c) 610

Answer key

  1. 8.9
  2. 7.7
  3. 27
  4. 74
  5. 8.5
  6. 36
  7. 68
  8. 4.7
  9. 32
  10. 24
  11. 7.8
  12. 86
  13. 5.9
  14. 7.1
  15. 29
  16. 9.1
  17. 5.6
  18. 56
  19. 8.1
  20. 4.5
  21. 92
  22. 34
  23. 93
  24. 62
  25. 82
  26. 27
  27. 25
  28. 9.1
  29. 70
  30. 4.8
  31. 50
  32. 49
  33. 82
  34. 8.7
  35. 8.3
  36. 8.4
  37. 80
  38. 71
  39. 63
  40. 61

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