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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 904 · 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.√34 to 1 decimal place? (a) 6.1 (b) 5.8 (c) 6.0 (d) 5.9
  2. 2.√50 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 7.3 (d) 7.4
  3. 3.Best estimate of 2258 ÷ 62? (a) 380 (b) 3800 (c) 38
  4. 4.√27 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 5.2 (d) 5.3
  5. 5.Best estimate of 4289 ÷ 56? (a) 710 (b) 7100 (c) 71
  6. 6.Best estimate of 3636 ÷ 52? (a) 7300 (b) 730 (c) 73
  7. 7.Best estimate of 1672 ÷ 44? (a) 420 (b) 42 (c) 4200
  8. 8.√67 to 1 decimal place? (a) 8.1 (b) 8.3 (c) 8.0 (d) 8.2
  9. 9.√80 to 1 decimal place? (a) 8.9 (b) 9.1 (c) 9.0 (d) 8.8
  10. 10.Best estimate of 2227 ÷ 73? (a) 3200 (b) 320 (c) 32
  11. 11.√74 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.5 (d) 8.7
  12. 12.√85 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.4 (d) 9.1
  13. 13.Best estimate of 3992 ÷ 79? (a) 500 (b) 50 (c) 5000
  14. 14.√32 to 1 decimal place? (a) 5.5 (b) 5.6 (c) 5.7 (d) 5.8
  15. 15.√88 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.2 (d) 9.3
  16. 16.Best estimate of 4952 ÷ 68? (a) 7100 (b) 71 (c) 710
  17. 17.Best estimate of 4317 ÷ 56? (a) 72 (b) 7200 (c) 720
  18. 18.Best estimate of 3537 ÷ 88? (a) 390 (b) 3900 (c) 39
  19. 19.Best estimate of 1906 ÷ 58? (a) 3200 (b) 32 (c) 320
  20. 20.√42 to 1 decimal place? (a) 6.8 (b) 6.7 (c) 6.5 (d) 6.6
  21. 21.√43 to 1 decimal place? (a) 6.8 (b) 6.6 (c) 6.5 (d) 6.7
  22. 22.√83 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.1 (d) 9.2
  23. 23.Best estimate of 3916 ÷ 46? (a) 780 (b) 7800 (c) 78
  24. 24.Best estimate of 1094 ÷ 37? (a) 2700 (b) 27 (c) 270
  25. 25.Best estimate of 3427 ÷ 76? (a) 43 (b) 430 (c) 4300
  26. 26.√90 to 1 decimal place? (a) 9.8 (b) 9.7 (c) 9.5 (d) 9.6
  27. 27.√24 to 1 decimal place? (a) 5.1 (b) 5.2 (c) 5.0 (d) 4.9
  28. 28.Best estimate of 1306 ÷ 39? (a) 330 (b) 3300 (c) 33
  29. 29.Best estimate of 567 ÷ 33? (a) 19 (b) 190 (c) 1900
  30. 30.Best estimate of 470 ÷ 39? (a) 120 (b) 12 (c) 1200
  31. 31.Best estimate of 1735 ÷ 67? (a) 250 (b) 25 (c) 2500
  32. 32.√71 to 1 decimal place? (a) 8.4 (b) 8.7 (c) 8.5 (d) 8.6
  33. 33.Best estimate of 601 ÷ 34? (a) 2000 (b) 20 (c) 200
  34. 34.Best estimate of 2309 ÷ 74? (a) 3300 (b) 33 (c) 330
  35. 35.Best estimate of 2538 ÷ 27? (a) 8500 (b) 85 (c) 850
  36. 36.Best estimate of 3700 ÷ 74? (a) 5300 (b) 530 (c) 53
  37. 37.Best estimate of 3843 ÷ 47? (a) 7700 (b) 770 (c) 77
  38. 38.√23 to 1 decimal place? (a) 4.7 (b) 4.6 (c) 4.8 (d) 4.9
  39. 39.√38 to 1 decimal place? (a) 6.0 (b) 6.2 (c) 5.9 (d) 6.1
  40. 40.Best estimate of 1661 ÷ 27? (a) 550 (b) 55 (c) 5500

Answer key

  1. 5.8
  2. 7.1
  3. 38
  4. 5.2
  5. 71
  6. 73
  7. 42
  8. 8.2
  9. 8.9
  10. 32
  11. 8.6
  12. 9.2
  13. 50
  14. 5.7
  15. 9.4
  16. 71
  17. 72
  18. 39
  19. 32
  20. 6.5
  21. 6.6
  22. 9.1
  23. 78
  24. 27
  25. 43
  26. 9.5
  27. 4.9
  28. 33
  29. 19
  30. 12
  31. 25
  32. 8.4
  33. 20
  34. 33
  35. 85
  36. 53
  37. 77
  38. 4.8
  39. 6.2
  40. 55

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