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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 55 · 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 4196 ÷ 61? (a) 700 (b) 7000 (c) 70
  2. 2.Best estimate of 898 ÷ 33? (a) 3000 (b) 30 (c) 300
  3. 3.Best estimate of 2474 ÷ 63? (a) 41 (b) 410 (c) 4100
  4. 4.Best estimate of 1519 ÷ 64? (a) 25 (b) 2500 (c) 250
  5. 5.√46 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 7.0 (d) 7.1
  6. 6.√43 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.7 (d) 6.8
  7. 7.√55 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.2 (d) 7.3
  8. 8.√59 to 1 decimal place? (a) 7.6 (b) 7.7 (c) 7.5 (d) 7.8
  9. 9.Best estimate of 2449 ÷ 77? (a) 3100 (b) 31 (c) 310
  10. 10.√71 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.5 (d) 8.4
  11. 11.Best estimate of 634 ÷ 27? (a) 210 (b) 21 (c) 2100
  12. 12.Best estimate of 5111 ÷ 87? (a) 57 (b) 570 (c) 5700
  13. 13.Best estimate of 1905 ÷ 46? (a) 38 (b) 380 (c) 3800
  14. 14.Best estimate of 3598 ÷ 48? (a) 720 (b) 7200 (c) 72
  15. 15.Best estimate of 2813 ÷ 49? (a) 560 (b) 5600 (c) 56
  16. 16.Best estimate of 2850 ÷ 62? (a) 480 (b) 4800 (c) 48
  17. 17.√35 to 1 decimal place? (a) 6.1 (b) 5.8 (c) 5.9 (d) 6.0
  18. 18.Best estimate of 6808 ÷ 87? (a) 76 (b) 7600 (c) 760
  19. 19.√51 to 1 decimal place? (a) 7.2 (b) 7.0 (c) 7.1 (d) 6.9
  20. 20.Best estimate of 1835 ÷ 81? (a) 230 (b) 23 (c) 2300
  21. 21.Best estimate of 5568 ÷ 68? (a) 8000 (b) 80 (c) 800
  22. 22.√31 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.6 (d) 5.7
  23. 23.Best estimate of 2122 ÷ 88? (a) 24 (b) 2400 (c) 240
  24. 24.Best estimate of 4042 ÷ 72? (a) 58 (b) 5800 (c) 580
  25. 25.√83 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 9.1 (d) 9.2
  26. 26.Best estimate of 1101 ÷ 23? (a) 550 (b) 5500 (c) 55
  27. 27.√98 to 1 decimal place? (a) 10.1 (b) 10.2 (c) 9.9 (d) 10.0
  28. 28.√30 to 1 decimal place? (a) 5.7 (b) 5.5 (c) 5.6 (d) 5.8
  29. 29.Best estimate of 1515 ÷ 26? (a) 51 (b) 5100 (c) 510
  30. 30.Best estimate of 2588 ÷ 72? (a) 3700 (b) 370 (c) 37
  31. 31.Best estimate of 853 ÷ 24? (a) 43 (b) 4300 (c) 430
  32. 32.Best estimate of 630 ÷ 28? (a) 2100 (b) 210 (c) 21
  33. 33.Best estimate of 1471 ÷ 44? (a) 37 (b) 3700 (c) 370
  34. 34.√63 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 7.8 (d) 8.1
  35. 35.Best estimate of 1902 ÷ 68? (a) 270 (b) 2700 (c) 27
  36. 36.√20 to 1 decimal place? (a) 4.3 (b) 4.2 (c) 4.4 (d) 4.5
  37. 37.Best estimate of 2087 ÷ 43? (a) 520 (b) 5200 (c) 52
  38. 38.Best estimate of 2010 ÷ 78? (a) 2500 (b) 250 (c) 25
  39. 39.√67 to 1 decimal place? (a) 7.9 (b) 8.1 (c) 8.2 (d) 8.0
  40. 40.Best estimate of 3096 ÷ 43? (a) 77 (b) 770 (c) 7700

Answer key

  1. 70
  2. 30
  3. 41
  4. 25
  5. 6.8
  6. 6.6
  7. 7.4
  8. 7.7
  9. 31
  10. 8.4
  11. 21
  12. 57
  13. 38
  14. 72
  15. 56
  16. 48
  17. 5.9
  18. 76
  19. 7.1
  20. 23
  21. 80
  22. 5.6
  23. 24
  24. 58
  25. 9.1
  26. 55
  27. 9.9
  28. 5.5
  29. 51
  30. 37
  31. 43
  32. 21
  33. 37
  34. 7.9
  35. 27
  36. 4.5
  37. 52
  38. 25
  39. 8.2
  40. 77

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