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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 511 · 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.√31 to 1 decimal place? (a) 5.4 (b) 5.6 (c) 5.3 (d) 5.5
  2. 2.√67 to 1 decimal place? (a) 8.5 (b) 8.2 (c) 8.3 (d) 8.4
  3. 3.√55 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.1 (d) 7.2
  4. 4.√72 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.4 (d) 8.5
  5. 5.Best estimate of 3114 ÷ 59? (a) 5200 (b) 52 (c) 520
  6. 6.Best estimate of 1023 ÷ 32? (a) 3400 (b) 34 (c) 340
  7. 7.Best estimate of 2567 ÷ 56? (a) 430 (b) 4300 (c) 43
  8. 8.Best estimate of 1133 ÷ 64? (a) 1900 (b) 19 (c) 190
  9. 9.√77 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.9 (d) 8.7
  10. 10.Best estimate of 1056 ÷ 66? (a) 15 (b) 150 (c) 1500
  11. 11.Best estimate of 1443 ÷ 49? (a) 290 (b) 29 (c) 2900
  12. 12.Best estimate of 870 ÷ 44? (a) 2200 (b) 22 (c) 220
  13. 13.Best estimate of 992 ÷ 22? (a) 50 (b) 5000 (c) 500
  14. 14.Best estimate of 1635 ÷ 32? (a) 550 (b) 5500 (c) 55
  15. 15.√98 to 1 decimal place? (a) 10.1 (b) 9.9 (c) 10.0 (d) 10.2
  16. 16.Best estimate of 1857 ÷ 26? (a) 620 (b) 62 (c) 6200
  17. 17.√83 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.4 (d) 9.3
  18. 18.Best estimate of 1317 ÷ 74? (a) 1900 (b) 19 (c) 190
  19. 19.Best estimate of 3200 ÷ 36? (a) 8000 (b) 80 (c) 800
  20. 20.Best estimate of 982 ÷ 32? (a) 3300 (b) 33 (c) 330
  21. 21.√30 to 1 decimal place? (a) 5.6 (b) 5.5 (c) 5.7 (d) 5.8
  22. 22.Best estimate of 3413 ÷ 39? (a) 85 (b) 850 (c) 8500
  23. 23.√92 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.3 (d) 9.6
  24. 24.√59 to 1 decimal place? (a) 7.7 (b) 7.9 (c) 7.6 (d) 7.8
  25. 25.√48 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.8 (d) 6.9
  26. 26.Best estimate of 2776 ÷ 77? (a) 350 (b) 35 (c) 3500
  27. 27.√28 to 1 decimal place? (a) 5.1 (b) 5.2 (c) 5.0 (d) 5.3
  28. 28.√47 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 7.2 (d) 7.1
  29. 29.√35 to 1 decimal place? (a) 6.1 (b) 6.0 (c) 5.8 (d) 5.9
  30. 30.√44 to 1 decimal place? (a) 6.7 (b) 6.5 (c) 6.6 (d) 6.8
  31. 31.√51 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 7.0 (d) 6.9
  32. 32.Best estimate of 942 ÷ 28? (a) 3100 (b) 31 (c) 310
  33. 33.√32 to 1 decimal place? (a) 5.5 (b) 5.7 (c) 5.6 (d) 5.4
  34. 34.√65 to 1 decimal place? (a) 7.8 (b) 8.0 (c) 8.1 (d) 7.9
  35. 35.√42 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.3 (d) 6.5
  36. 36.√96 to 1 decimal place? (a) 9.8 (b) 9.5 (c) 9.6 (d) 9.7
  37. 37.Best estimate of 6732 ÷ 83? (a) 84 (b) 8400 (c) 840
  38. 38.Best estimate of 2574 ÷ 42? (a) 640 (b) 6400 (c) 64
  39. 39.Best estimate of 1502 ÷ 86? (a) 1700 (b) 170 (c) 17
  40. 40.√71 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.2 (d) 8.1

Answer key

  1. 5.6
  2. 8.2
  3. 7.4
  4. 8.5
  5. 52
  6. 34
  7. 43
  8. 19
  9. 8.8
  10. 15
  11. 29
  12. 22
  13. 50
  14. 55
  15. 9.9
  16. 62
  17. 9.1
  18. 19
  19. 80
  20. 33
  21. 5.5
  22. 85
  23. 9.6
  24. 7.7
  25. 6.9
  26. 35
  27. 5.3
  28. 6.9
  29. 5.9
  30. 6.6
  31. 7.1
  32. 31
  33. 5.7
  34. 8.1
  35. 6.5
  36. 9.8
  37. 84
  38. 64
  39. 17
  40. 8.4

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