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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 133 · 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) 7.5 (c) 7.3 (d) 7.6
  2. 2.√48 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 7.2 (d) 6.9
  3. 3.√98 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.8 (d) 9.9
  4. 4.Best estimate of 3674 ÷ 43? (a) 92 (b) 9200 (c) 920
  5. 5.Best estimate of 2218 ÷ 62? (a) 370 (b) 37 (c) 3700
  6. 6.Best estimate of 3078 ÷ 86? (a) 340 (b) 34 (c) 3400
  7. 7.√80 to 1 decimal place? (a) 9.2 (b) 8.9 (c) 9.0 (d) 9.1
  8. 8.√38 to 1 decimal place? (a) 6.5 (b) 6.4 (c) 6.2 (d) 6.3
  9. 9.Best estimate of 1686 ÷ 28? (a) 56 (b) 560 (c) 5600
  10. 10.√20 to 1 decimal place? (a) 4.5 (b) 4.6 (c) 4.8 (d) 4.7
  11. 11.√26 to 1 decimal place? (a) 5.0 (b) 5.3 (c) 5.1 (d) 5.2
  12. 12.√89 to 1 decimal place? (a) 9.7 (b) 9.5 (c) 9.6 (d) 9.4
  13. 13.Best estimate of 365 ÷ 24? (a) 1800 (b) 180 (c) 18
  14. 14.√82 to 1 decimal place? (a) 9.1 (b) 9.3 (c) 9.4 (d) 9.2
  15. 15.Best estimate of 1709 ÷ 36? (a) 4300 (b) 43 (c) 430
  16. 16.Best estimate of 2940 ÷ 82? (a) 37 (b) 3700 (c) 370
  17. 17.√86 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.3 (d) 9.6
  18. 18.Best estimate of 6007 ÷ 64? (a) 100 (b) 1000 (c) 10000
  19. 19.√52 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 7.3 (d) 7.0
  20. 20.Best estimate of 5204 ÷ 59? (a) 870 (b) 8700 (c) 87
  21. 21.Best estimate of 2364 ÷ 56? (a) 3900 (b) 39 (c) 390
  22. 22.Best estimate of 6553 ÷ 82? (a) 82 (b) 820 (c) 8200
  23. 23.√45 to 1 decimal place? (a) 6.8 (b) 6.5 (c) 6.6 (d) 6.7
  24. 24.Best estimate of 1515 ÷ 71? (a) 220 (b) 22 (c) 2200
  25. 25.Best estimate of 1248 ÷ 56? (a) 2100 (b) 21 (c) 210
  26. 26.√34 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.9 (d) 5.8
  27. 27.√27 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.2 (d) 5.3
  28. 28.√92 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.5 (d) 9.8
  29. 29.√78 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 9.0 (d) 8.7
  30. 30.Best estimate of 350 ÷ 24? (a) 1800 (b) 180 (c) 18
  31. 31.√43 to 1 decimal place? (a) 6.9 (b) 6.6 (c) 6.8 (d) 6.7
  32. 32.Best estimate of 1495 ÷ 21? (a) 7500 (b) 75 (c) 750
  33. 33.√75 to 1 decimal place? (a) 8.7 (b) 8.5 (c) 8.4 (d) 8.6
  34. 34.Best estimate of 933 ÷ 49? (a) 190 (b) 1900 (c) 19
  35. 35.√66 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.4 (d) 8.1
  36. 36.Best estimate of 1822 ÷ 57? (a) 3000 (b) 30 (c) 300
  37. 37.Best estimate of 1207 ÷ 22? (a) 600 (b) 60 (c) 6000
  38. 38.√58 to 1 decimal place? (a) 7.7 (b) 7.9 (c) 7.8 (d) 7.6
  39. 39.Best estimate of 2166 ÷ 87? (a) 240 (b) 24 (c) 2400
  40. 40.Best estimate of 3674 ÷ 86? (a) 41 (b) 4100 (c) 410

Answer key

  1. 7.4
  2. 6.9
  3. 9.9
  4. 92
  5. 37
  6. 34
  7. 8.9
  8. 6.2
  9. 56
  10. 4.5
  11. 5.1
  12. 9.4
  13. 18
  14. 9.1
  15. 43
  16. 37
  17. 9.3
  18. 100
  19. 7.2
  20. 87
  21. 39
  22. 82
  23. 6.7
  24. 22
  25. 21
  26. 5.8
  27. 5.2
  28. 9.6
  29. 8.8
  30. 18
  31. 6.6
  32. 75
  33. 8.7
  34. 19
  35. 8.1
  36. 30
  37. 60
  38. 7.6
  39. 24
  40. 41

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