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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 97 · 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.√58 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.4 (d) 7.3
  2. 2.Best estimate of 4314 ÷ 63? (a) 72 (b) 7200 (c) 720
  3. 3.Best estimate of 2215 ÷ 83? (a) 28 (b) 280 (c) 2800
  4. 4.√53 to 1 decimal place? (a) 7.5 (b) 7.2 (c) 7.4 (d) 7.3
  5. 5.√34 to 1 decimal place? (a) 5.8 (b) 6.0 (c) 6.1 (d) 5.9
  6. 6.√59 to 1 decimal place? (a) 8.0 (b) 7.9 (c) 7.7 (d) 7.8
  7. 7.√38 to 1 decimal place? (a) 6.0 (b) 6.1 (c) 6.2 (d) 6.3
  8. 8.Best estimate of 636 ÷ 31? (a) 21 (b) 210 (c) 2100
  9. 9.Best estimate of 1729 ÷ 47? (a) 35 (b) 3500 (c) 350
  10. 10.√27 to 1 decimal place? (a) 5.0 (b) 5.3 (c) 5.1 (d) 5.2
  11. 11.Best estimate of 479 ÷ 34? (a) 160 (b) 1600 (c) 16
  12. 12.Best estimate of 1177 ÷ 33? (a) 39 (b) 3900 (c) 390
  13. 13.Best estimate of 3084 ÷ 86? (a) 3400 (b) 340 (c) 34
  14. 14.√35 to 1 decimal place? (a) 5.6 (b) 5.8 (c) 5.7 (d) 5.9
  15. 15.Best estimate of 2396 ÷ 74? (a) 34 (b) 340 (c) 3400
  16. 16.√46 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 7.0 (d) 6.9
  17. 17.√55 to 1 decimal place? (a) 7.5 (b) 7.3 (c) 7.2 (d) 7.4
  18. 18.√43 to 1 decimal place? (a) 6.4 (b) 6.6 (c) 6.3 (d) 6.5
  19. 19.Best estimate of 3652 ÷ 42? (a) 910 (b) 91 (c) 9100
  20. 20.Best estimate of 1211 ÷ 41? (a) 300 (b) 3000 (c) 30
  21. 21.Best estimate of 8100 ÷ 86? (a) 900 (b) 90 (c) 9000
  22. 22.Best estimate of 5166 ÷ 76? (a) 65 (b) 6500 (c) 650
  23. 23.Best estimate of 1082 ÷ 27? (a) 3600 (b) 360 (c) 36
  24. 24.Best estimate of 5246 ÷ 86? (a) 58 (b) 580 (c) 5800
  25. 25.Best estimate of 1544 ÷ 33? (a) 5100 (b) 51 (c) 510
  26. 26.Best estimate of 582 ÷ 32? (a) 1900 (b) 19 (c) 190
  27. 27.√26 to 1 decimal place? (a) 5.2 (b) 5.3 (c) 5.1 (d) 5.0
  28. 28.√70 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.1 (d) 8.2
  29. 29.Best estimate of 3152 ÷ 41? (a) 790 (b) 7900 (c) 79
  30. 30.Best estimate of 1041 ÷ 57? (a) 170 (b) 1700 (c) 17
  31. 31.Best estimate of 6827 ÷ 83? (a) 850 (b) 8500 (c) 85
  32. 32.Best estimate of 2096 ÷ 62? (a) 3500 (b) 35 (c) 350
  33. 33.Best estimate of 3153 ÷ 33? (a) 105 (b) 1050 (c) 10500
  34. 34.Best estimate of 2205 ÷ 36? (a) 550 (b) 5500 (c) 55
  35. 35.√90 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.7 (d) 9.6
  36. 36.Best estimate of 4215 ÷ 46? (a) 84 (b) 840 (c) 8400
  37. 37.Best estimate of 4322 ÷ 58? (a) 72 (b) 720 (c) 7200
  38. 38.Best estimate of 1932 ÷ 36? (a) 48 (b) 480 (c) 4800
  39. 39.Best estimate of 1479 ÷ 34? (a) 49 (b) 490 (c) 4900
  40. 40.√92 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.7 (d) 9.6

Answer key

  1. 7.6
  2. 72
  3. 28
  4. 7.3
  5. 5.8
  6. 7.7
  7. 6.2
  8. 21
  9. 35
  10. 5.2
  11. 16
  12. 39
  13. 34
  14. 5.9
  15. 34
  16. 6.8
  17. 7.4
  18. 6.6
  19. 91
  20. 30
  21. 90
  22. 65
  23. 36
  24. 58
  25. 51
  26. 19
  27. 5.1
  28. 8.4
  29. 79
  30. 17
  31. 85
  32. 35
  33. 105
  34. 55
  35. 9.5
  36. 84
  37. 72
  38. 48
  39. 49
  40. 9.6

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