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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 350 · 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.√23 to 1 decimal place? (a) 4.7 (b) 4.8 (c) 4.5 (d) 4.6
  2. 2.Best estimate of 3449 ÷ 83? (a) 430 (b) 4300 (c) 43
  3. 3.Best estimate of 1386 ÷ 32? (a) 460 (b) 4600 (c) 46
  4. 4.√84 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.4 (d) 9.1
  5. 5.√31 to 1 decimal place? (a) 5.9 (b) 5.8 (c) 5.6 (d) 5.7
  6. 6.Best estimate of 1379 ÷ 26? (a) 4600 (b) 460 (c) 46
  7. 7.Best estimate of 1392 ÷ 36? (a) 3500 (b) 35 (c) 350
  8. 8.√67 to 1 decimal place? (a) 8.0 (b) 8.2 (c) 8.1 (d) 7.9
  9. 9.Best estimate of 2876 ÷ 38? (a) 7200 (b) 72 (c) 720
  10. 10.Best estimate of 3844 ÷ 72? (a) 5500 (b) 55 (c) 550
  11. 11.√61 to 1 decimal place? (a) 8.0 (b) 7.9 (c) 7.8 (d) 7.7
  12. 12.√47 to 1 decimal place? (a) 7.2 (b) 6.9 (c) 7.0 (d) 7.1
  13. 13.√71 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.4 (d) 8.5
  14. 14.√89 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.1 (d) 9.2
  15. 15.Best estimate of 2147 ÷ 26? (a) 72 (b) 720 (c) 7200
  16. 16.Best estimate of 3504 ÷ 72? (a) 5000 (b) 500 (c) 50
  17. 17.Best estimate of 5758 ÷ 81? (a) 7200 (b) 72 (c) 720
  18. 18.Best estimate of 5655 ÷ 87? (a) 63 (b) 6300 (c) 630
  19. 19.Best estimate of 1124 ÷ 63? (a) 19 (b) 190 (c) 1900
  20. 20.Best estimate of 4148 ÷ 67? (a) 59 (b) 5900 (c) 590
  21. 21.Best estimate of 2627 ÷ 53? (a) 530 (b) 53 (c) 5300
  22. 22.Best estimate of 3194 ÷ 48? (a) 64 (b) 6400 (c) 640
  23. 23.√43 to 1 decimal place? (a) 6.6 (b) 6.3 (c) 6.5 (d) 6.4
  24. 24.√98 to 1 decimal place? (a) 10.0 (b) 9.8 (c) 9.9 (d) 10.1
  25. 25.Best estimate of 6210 ÷ 69? (a) 890 (b) 8900 (c) 89
  26. 26.√40 to 1 decimal place? (a) 6.0 (b) 6.1 (c) 6.2 (d) 6.3
  27. 27.√38 to 1 decimal place? (a) 6.2 (b) 6.0 (c) 6.3 (d) 6.1
  28. 28.√50 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 6.9 (d) 7.0
  29. 29.√37 to 1 decimal place? (a) 6.1 (b) 6.3 (c) 6.0 (d) 6.2
  30. 30.Best estimate of 2478 ÷ 68? (a) 350 (b) 3500 (c) 35
  31. 31.Best estimate of 3477 ÷ 81? (a) 430 (b) 43 (c) 4300
  32. 32.Best estimate of 2822 ÷ 71? (a) 400 (b) 4000 (c) 40
  33. 33.Best estimate of 2509 ÷ 89? (a) 2800 (b) 280 (c) 28
  34. 34.√55 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 7.4 (d) 7.3
  35. 35.√58 to 1 decimal place? (a) 7.5 (b) 7.8 (c) 7.6 (d) 7.7
  36. 36.√28 to 1 decimal place? (a) 5.2 (b) 5.3 (c) 5.0 (d) 5.1
  37. 37.√65 to 1 decimal place? (a) 8.3 (b) 8.1 (c) 8.2 (d) 8.0
  38. 38.√34 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 6.0 (d) 5.7
  39. 39.Best estimate of 799 ÷ 33? (a) 27 (b) 270 (c) 2700
  40. 40.Best estimate of 1999 ÷ 36? (a) 50 (b) 500 (c) 5000

Answer key

  1. 4.8
  2. 43
  3. 46
  4. 9.2
  5. 5.6
  6. 46
  7. 35
  8. 8.2
  9. 72
  10. 55
  11. 7.8
  12. 6.9
  13. 8.4
  14. 9.4
  15. 72
  16. 50
  17. 72
  18. 63
  19. 19
  20. 59
  21. 53
  22. 64
  23. 6.6
  24. 9.9
  25. 89
  26. 6.3
  27. 6.2
  28. 7.1
  29. 6.1
  30. 35
  31. 43
  32. 40
  33. 28
  34. 7.4
  35. 7.6
  36. 5.3
  37. 8.1
  38. 5.8
  39. 27
  40. 50

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