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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 960 · 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.Best estimate of 3949 ÷ 44? (a) 990 (b) 9900 (c) 99
  2. 2.√79 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 9.1 (d) 8.9
  3. 3.Best estimate of 4836 ÷ 53? (a) 97 (b) 9700 (c) 970
  4. 4.√98 to 1 decimal place? (a) 10.0 (b) 10.2 (c) 10.1 (d) 9.9
  5. 5.√20 to 1 decimal place? (a) 4.6 (b) 4.5 (c) 4.4 (d) 4.7
  6. 6.Best estimate of 1633 ÷ 36? (a) 4100 (b) 410 (c) 41
  7. 7.√70 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.1 (d) 8.4
  8. 8.√26 to 1 decimal place? (a) 5.4 (b) 5.1 (c) 5.3 (d) 5.2
  9. 9.√85 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.0 (d) 9.1
  10. 10.√34 to 1 decimal place? (a) 5.9 (b) 5.8 (c) 5.7 (d) 6.0
  11. 11.Best estimate of 3153 ÷ 81? (a) 390 (b) 39 (c) 3900
  12. 12.√78 to 1 decimal place? (a) 8.8 (b) 9.0 (c) 8.9 (d) 8.7
  13. 13.√58 to 1 decimal place? (a) 7.4 (b) 7.6 (c) 7.5 (d) 7.3
  14. 14.√55 to 1 decimal place? (a) 7.5 (b) 7.2 (c) 7.4 (d) 7.3
  15. 15.√30 to 1 decimal place? (a) 5.6 (b) 5.3 (c) 5.4 (d) 5.5
  16. 16.Best estimate of 2185 ÷ 86? (a) 240 (b) 24 (c) 2400
  17. 17.Best estimate of 1401 ÷ 56? (a) 230 (b) 23 (c) 2300
  18. 18.Best estimate of 1117 ÷ 22? (a) 56 (b) 560 (c) 5600
  19. 19.√62 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 7.9 (d) 8.2
  20. 20.Best estimate of 417 ÷ 26? (a) 14 (b) 140 (c) 1400
  21. 21.Best estimate of 3294 ÷ 46? (a) 66 (b) 660 (c) 6600
  22. 22.√50 to 1 decimal place? (a) 7.0 (b) 6.9 (c) 7.1 (d) 6.8
  23. 23.Best estimate of 3569 ÷ 71? (a) 510 (b) 5100 (c) 51
  24. 24.√74 to 1 decimal place? (a) 8.7 (b) 8.4 (c) 8.6 (d) 8.5
  25. 25.√90 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.4 (d) 9.7
  26. 26.Best estimate of 2408 ÷ 77? (a) 300 (b) 30 (c) 3000
  27. 27.√41 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.3 (d) 6.5
  28. 28.Best estimate of 990 ÷ 33? (a) 33 (b) 3300 (c) 330
  29. 29.√40 to 1 decimal place? (a) 6.5 (b) 6.4 (c) 6.3 (d) 6.6
  30. 30.Best estimate of 3747 ÷ 74? (a) 540 (b) 54 (c) 5400
  31. 31.√23 to 1 decimal place? (a) 4.9 (b) 4.7 (c) 4.6 (d) 4.8
  32. 32.Best estimate of 1951 ÷ 78? (a) 240 (b) 24 (c) 2400
  33. 33.√46 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 6.8 (d) 7.1
  34. 34.Best estimate of 1453 ÷ 31? (a) 4800 (b) 48 (c) 480
  35. 35.√45 to 1 decimal place? (a) 6.9 (b) 6.7 (c) 7.0 (d) 6.8
  36. 36.√65 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 8.1 (d) 8.0
  37. 37.Best estimate of 1785 ÷ 51? (a) 36 (b) 360 (c) 3600
  38. 38.√53 to 1 decimal place? (a) 7.2 (b) 7.4 (c) 7.3 (d) 7.1
  39. 39.Best estimate of 3072 ÷ 87? (a) 3400 (b) 340 (c) 34
  40. 40.√76 to 1 decimal place? (a) 8.8 (b) 8.7 (c) 8.9 (d) 8.6

Answer key

  1. 99
  2. 8.9
  3. 97
  4. 9.9
  5. 4.5
  6. 41
  7. 8.4
  8. 5.1
  9. 9.2
  10. 5.8
  11. 39
  12. 8.8
  13. 7.6
  14. 7.4
  15. 5.5
  16. 24
  17. 23
  18. 56
  19. 7.9
  20. 14
  21. 66
  22. 7.1
  23. 51
  24. 8.6
  25. 9.5
  26. 30
  27. 6.4
  28. 33
  29. 6.3
  30. 54
  31. 4.8
  32. 24
  33. 6.8
  34. 48
  35. 6.7
  36. 8.1
  37. 36
  38. 7.3
  39. 34
  40. 8.7

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