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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 558 · 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 2471 ÷ 39? (a) 6200 (b) 62 (c) 620
  2. 2.Best estimate of 7084 ÷ 74? (a) 1010 (b) 101 (c) 10100
  3. 3.√92 to 1 decimal place? (a) 9.6 (b) 9.8 (c) 9.9 (d) 9.7
  4. 4.Best estimate of 2398 ÷ 26? (a) 80 (b) 800 (c) 8000
  5. 5.√50 to 1 decimal place? (a) 7.1 (b) 6.9 (c) 7.0 (d) 7.2
  6. 6.√34 to 1 decimal place? (a) 5.9 (b) 5.7 (c) 5.6 (d) 5.8
  7. 7.√24 to 1 decimal place? (a) 4.8 (b) 4.7 (c) 4.6 (d) 4.9
  8. 8.Best estimate of 1671 ÷ 39? (a) 42 (b) 420 (c) 4200
  9. 9.√76 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.6 (d) 8.7
  10. 10.Best estimate of 866 ÷ 26? (a) 2900 (b) 290 (c) 29
  11. 11.Best estimate of 1402 ÷ 38? (a) 35 (b) 3500 (c) 350
  12. 12.√72 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.5 (d) 8.4
  13. 13.√69 to 1 decimal place? (a) 8.3 (b) 8.5 (c) 8.6 (d) 8.4
  14. 14.√27 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.1 (d) 5.0
  15. 15.√38 to 1 decimal place? (a) 6.1 (b) 6.2 (c) 5.9 (d) 6.0
  16. 16.√98 to 1 decimal place? (a) 9.9 (b) 10.1 (c) 10.0 (d) 10.2
  17. 17.Best estimate of 2132 ÷ 68? (a) 3000 (b) 300 (c) 30
  18. 18.Best estimate of 4288 ÷ 81? (a) 540 (b) 5400 (c) 54
  19. 19.√26 to 1 decimal place? (a) 4.9 (b) 4.8 (c) 5.0 (d) 5.1
  20. 20.√41 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.5 (d) 6.4
  21. 21.Best estimate of 1436 ÷ 67? (a) 2100 (b) 210 (c) 21
  22. 22.Best estimate of 2959 ÷ 46? (a) 59 (b) 590 (c) 5900
  23. 23.√82 to 1 decimal place? (a) 8.9 (b) 9.2 (c) 9.1 (d) 9.0
  24. 24.Best estimate of 754 ÷ 37? (a) 19 (b) 1900 (c) 190
  25. 25.√79 to 1 decimal place? (a) 8.8 (b) 9.1 (c) 8.9 (d) 9.0
  26. 26.Best estimate of 6498 ÷ 69? (a) 930 (b) 9300 (c) 93
  27. 27.√47 to 1 decimal place? (a) 7.0 (b) 6.8 (c) 6.7 (d) 6.9
  28. 28.Best estimate of 1523 ÷ 31? (a) 510 (b) 5100 (c) 51
  29. 29.Best estimate of 4326 ÷ 54? (a) 87 (b) 8700 (c) 870
  30. 30.Best estimate of 1768 ÷ 26? (a) 590 (b) 5900 (c) 59
  31. 31.Best estimate of 3357 ÷ 52? (a) 6700 (b) 67 (c) 670
  32. 32.√74 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.8 (d) 8.5
  33. 33.√48 to 1 decimal place? (a) 7.0 (b) 7.1 (c) 6.9 (d) 7.2
  34. 34.Best estimate of 2489 ÷ 36? (a) 6200 (b) 620 (c) 62
  35. 35.Best estimate of 2937 ÷ 66? (a) 42 (b) 4200 (c) 420
  36. 36.√21 to 1 decimal place? (a) 4.3 (b) 4.5 (c) 4.6 (d) 4.4
  37. 37.Best estimate of 578 ÷ 42? (a) 1400 (b) 14 (c) 140
  38. 38.√44 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.8 (d) 6.5
  39. 39.√94 to 1 decimal place? (a) 9.9 (b) 10.0 (c) 9.7 (d) 9.8
  40. 40.√53 to 1 decimal place? (a) 7.3 (b) 7.1 (c) 7.2 (d) 7.4

Answer key

  1. 62
  2. 101
  3. 9.6
  4. 80
  5. 7.1
  6. 5.8
  7. 4.9
  8. 42
  9. 8.7
  10. 29
  11. 35
  12. 8.5
  13. 8.3
  14. 5.2
  15. 6.2
  16. 9.9
  17. 30
  18. 54
  19. 5.1
  20. 6.4
  21. 21
  22. 59
  23. 9.1
  24. 19
  25. 8.9
  26. 93
  27. 6.9
  28. 51
  29. 87
  30. 59
  31. 67
  32. 8.6
  33. 6.9
  34. 62
  35. 42
  36. 4.6
  37. 14
  38. 6.6
  39. 9.7
  40. 7.3

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