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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 621 · 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.√71 to 1 decimal place? (a) 8.1 (b) 8.4 (c) 8.3 (d) 8.2
  2. 2.Best estimate of 958 ÷ 68? (a) 140 (b) 14 (c) 1400
  3. 3.√26 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.2 (d) 5.1
  4. 4.Best estimate of 861 ÷ 42? (a) 220 (b) 2200 (c) 22
  5. 5.Best estimate of 1517 ÷ 24? (a) 7600 (b) 76 (c) 760
  6. 6.√63 to 1 decimal place? (a) 7.9 (b) 8.2 (c) 8.1 (d) 8.0
  7. 7.Best estimate of 2117 ÷ 32? (a) 710 (b) 7100 (c) 71
  8. 8.Best estimate of 4100 ÷ 52? (a) 8200 (b) 820 (c) 82
  9. 9.√76 to 1 decimal place? (a) 8.8 (b) 9.0 (c) 8.9 (d) 8.7
  10. 10.Best estimate of 1783 ÷ 32? (a) 590 (b) 5900 (c) 59
  11. 11.√42 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.6 (d) 6.5
  12. 12.Best estimate of 1345 ÷ 61? (a) 220 (b) 22 (c) 2200
  13. 13.√92 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.8 (d) 9.9
  14. 14.Best estimate of 1123 ÷ 51? (a) 2200 (b) 220 (c) 22
  15. 15.√30 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.6 (d) 5.5
  16. 16.√75 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 8.6 (d) 8.7
  17. 17.Best estimate of 1257 ÷ 39? (a) 3100 (b) 310 (c) 31
  18. 18.√89 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.3 (d) 9.5
  19. 19.Best estimate of 1302 ÷ 33? (a) 430 (b) 4300 (c) 43
  20. 20.√84 to 1 decimal place? (a) 9.5 (b) 9.2 (c) 9.3 (d) 9.4
  21. 21.√46 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.9 (d) 6.6
  22. 22.Best estimate of 4016 ÷ 76? (a) 500 (b) 5000 (c) 50
  23. 23.Best estimate of 2195 ÷ 58? (a) 37 (b) 3700 (c) 370
  24. 24.√53 to 1 decimal place? (a) 7.3 (b) 7.5 (c) 7.4 (d) 7.2
  25. 25.Best estimate of 2091 ÷ 62? (a) 350 (b) 3500 (c) 35
  26. 26.√85 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.2 (d) 9.5
  27. 27.Best estimate of 3268 ÷ 46? (a) 650 (b) 6500 (c) 65
  28. 28.√55 to 1 decimal place? (a) 7.3 (b) 7.5 (c) 7.2 (d) 7.4
  29. 29.Best estimate of 4673 ÷ 79? (a) 5800 (b) 580 (c) 58
  30. 30.√43 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.8 (d) 6.7
  31. 31.Best estimate of 3388 ÷ 63? (a) 560 (b) 5600 (c) 56
  32. 32.Best estimate of 1383 ÷ 87? (a) 1500 (b) 15 (c) 150
  33. 33.√40 to 1 decimal place? (a) 6.4 (b) 6.2 (c) 6.1 (d) 6.3
  34. 34.√38 to 1 decimal place? (a) 6.4 (b) 6.2 (c) 6.5 (d) 6.3
  35. 35.Best estimate of 7022 ÷ 76? (a) 880 (b) 88 (c) 8800
  36. 36.√50 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 6.9 (d) 6.8
  37. 37.√65 to 1 decimal place? (a) 8.2 (b) 8.4 (c) 8.3 (d) 8.1
  38. 38.Best estimate of 3183 ÷ 46? (a) 64 (b) 640 (c) 6400
  39. 39.Best estimate of 1934 ÷ 31? (a) 640 (b) 6400 (c) 64
  40. 40.Best estimate of 2108 ÷ 43? (a) 530 (b) 53 (c) 5300

Answer key

  1. 8.4
  2. 14
  3. 5.1
  4. 22
  5. 76
  6. 7.9
  7. 71
  8. 82
  9. 8.7
  10. 59
  11. 6.5
  12. 22
  13. 9.6
  14. 22
  15. 5.5
  16. 8.7
  17. 31
  18. 9.4
  19. 43
  20. 9.2
  21. 6.8
  22. 50
  23. 37
  24. 7.3
  25. 35
  26. 9.2
  27. 65
  28. 7.4
  29. 58
  30. 6.6
  31. 56
  32. 15
  33. 6.3
  34. 6.2
  35. 88
  36. 7.1
  37. 8.1
  38. 64
  39. 64
  40. 53

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