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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 278 · 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.√78 to 1 decimal place? (a) 9.1 (b) 8.9 (c) 8.8 (d) 9.0
  2. 2.√61 to 1 decimal place? (a) 8.0 (b) 7.9 (c) 7.8 (d) 8.1
  3. 3.Best estimate of 1344 ÷ 36? (a) 34 (b) 3400 (c) 340
  4. 4.Best estimate of 3535 ÷ 86? (a) 3900 (b) 390 (c) 39
  5. 5.Best estimate of 706 ÷ 33? (a) 2400 (b) 240 (c) 24
  6. 6.Best estimate of 4637 ÷ 66? (a) 6600 (b) 66 (c) 660
  7. 7.√79 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.7 (d) 8.9
  8. 8.√96 to 1 decimal place? (a) 10.0 (b) 10.1 (c) 9.9 (d) 9.8
  9. 9.√74 to 1 decimal place? (a) 8.7 (b) 8.5 (c) 8.8 (d) 8.6
  10. 10.Best estimate of 2050 ÷ 46? (a) 41 (b) 4100 (c) 410
  11. 11.√70 to 1 decimal place? (a) 8.2 (b) 8.4 (c) 8.1 (d) 8.3
  12. 12.Best estimate of 4653 ÷ 54? (a) 9300 (b) 93 (c) 930
  13. 13.Best estimate of 2697 ÷ 88? (a) 30 (b) 3000 (c) 300
  14. 14.√40 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.4 (d) 6.5
  15. 15.√37 to 1 decimal place? (a) 6.0 (b) 5.9 (c) 6.2 (d) 6.1
  16. 16.Best estimate of 672 ÷ 32? (a) 22 (b) 2200 (c) 220
  17. 17.√41 to 1 decimal place? (a) 6.3 (b) 6.6 (c) 6.4 (d) 6.5
  18. 18.√51 to 1 decimal place? (a) 7.3 (b) 7.2 (c) 7.1 (d) 7.0
  19. 19.Best estimate of 712 ÷ 54? (a) 14 (b) 1400 (c) 140
  20. 20.Best estimate of 3347 ÷ 79? (a) 420 (b) 42 (c) 4200
  21. 21.Best estimate of 1877 ÷ 26? (a) 63 (b) 630 (c) 6300
  22. 22.Best estimate of 1033 ÷ 24? (a) 5200 (b) 520 (c) 52
  23. 23.Best estimate of 1190 ÷ 74? (a) 1700 (b) 170 (c) 17
  24. 24.Best estimate of 2302 ÷ 32? (a) 770 (b) 7700 (c) 77
  25. 25.Best estimate of 5408 ÷ 58? (a) 9000 (b) 900 (c) 90
  26. 26.Best estimate of 1376 ÷ 54? (a) 28 (b) 280 (c) 2800
  27. 27.√32 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.5 (d) 5.6
  28. 28.√87 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.5 (d) 9.6
  29. 29.Best estimate of 1522 ÷ 26? (a) 51 (b) 5100 (c) 510
  30. 30.Best estimate of 2970 ÷ 49? (a) 59 (b) 5900 (c) 590
  31. 31.Best estimate of 973 ÷ 27? (a) 32 (b) 3200 (c) 320
  32. 32.√94 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 9.7 (d) 9.6
  33. 33.√55 to 1 decimal place? (a) 7.3 (b) 7.1 (c) 7.4 (d) 7.2
  34. 34.√58 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.6 (d) 7.5
  35. 35.√98 to 1 decimal place? (a) 10.1 (b) 9.8 (c) 10.0 (d) 9.9
  36. 36.Best estimate of 1994 ÷ 26? (a) 660 (b) 6600 (c) 66
  37. 37.Best estimate of 2596 ÷ 38? (a) 65 (b) 650 (c) 6500
  38. 38.Best estimate of 4984 ÷ 82? (a) 6200 (b) 62 (c) 620
  39. 39.√38 to 1 decimal place? (a) 6.4 (b) 6.1 (c) 6.2 (d) 6.3
  40. 40.√34 to 1 decimal place? (a) 5.7 (b) 5.9 (c) 5.6 (d) 5.8

Answer key

  1. 8.8
  2. 7.8
  3. 34
  4. 39
  5. 24
  6. 66
  7. 8.9
  8. 9.8
  9. 8.6
  10. 41
  11. 8.4
  12. 93
  13. 30
  14. 6.3
  15. 6.1
  16. 22
  17. 6.4
  18. 7.1
  19. 14
  20. 42
  21. 63
  22. 52
  23. 17
  24. 77
  25. 90
  26. 28
  27. 5.7
  28. 9.3
  29. 51
  30. 59
  31. 32
  32. 9.7
  33. 7.4
  34. 7.6
  35. 9.9
  36. 66
  37. 65
  38. 62
  39. 6.2
  40. 5.8

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