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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 448 · 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.√75 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.9 (d) 8.8
  2. 2.Best estimate of 955 ÷ 31? (a) 320 (b) 3200 (c) 32
  3. 3.Best estimate of 1892 ÷ 69? (a) 27 (b) 2700 (c) 270
  4. 4.Best estimate of 5050 ÷ 58? (a) 840 (b) 84 (c) 8400
  5. 5.Best estimate of 1045 ÷ 42? (a) 260 (b) 2600 (c) 26
  6. 6.√48 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 7.0 (d) 6.7
  7. 7.Best estimate of 980 ÷ 33? (a) 33 (b) 330 (c) 3300
  8. 8.√90 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 9.6 (d) 9.5
  9. 9.Best estimate of 2633 ÷ 72? (a) 3800 (b) 380 (c) 38
  10. 10.√26 to 1 decimal place? (a) 4.9 (b) 5.0 (c) 4.8 (d) 5.1
  11. 11.√92 to 1 decimal place? (a) 9.7 (b) 9.5 (c) 9.6 (d) 9.8
  12. 12.√21 to 1 decimal place? (a) 4.5 (b) 4.4 (c) 4.6 (d) 4.3
  13. 13.Best estimate of 4871 ÷ 86? (a) 540 (b) 54 (c) 5400
  14. 14.√84 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.1 (d) 9.0
  15. 15.√89 to 1 decimal place? (a) 9.5 (b) 9.7 (c) 9.6 (d) 9.4
  16. 16.√42 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.3 (d) 6.2
  17. 17.Best estimate of 1941 ÷ 66? (a) 2800 (b) 280 (c) 28
  18. 18.Best estimate of 2901 ÷ 74? (a) 4100 (b) 41 (c) 410
  19. 19.Best estimate of 6530 ÷ 84? (a) 8200 (b) 82 (c) 820
  20. 20.Best estimate of 6382 ÷ 86? (a) 71 (b) 710 (c) 7100
  21. 21.Best estimate of 4409 ÷ 62? (a) 7300 (b) 73 (c) 730
  22. 22.Best estimate of 4936 ÷ 82? (a) 620 (b) 6200 (c) 62
  23. 23.√69 to 1 decimal place? (a) 8.5 (b) 8.3 (c) 8.2 (d) 8.4
  24. 24.√65 to 1 decimal place? (a) 8.0 (b) 8.2 (c) 8.1 (d) 7.9
  25. 25.Best estimate of 3576 ÷ 42? (a) 8900 (b) 89 (c) 890
  26. 26.Best estimate of 3369 ÷ 52? (a) 67 (b) 670 (c) 6700
  27. 27.Best estimate of 2544 ÷ 72? (a) 360 (b) 36 (c) 3600
  28. 28.Best estimate of 6469 ÷ 73? (a) 920 (b) 92 (c) 9200
  29. 29.√88 to 1 decimal place? (a) 9.4 (b) 9.6 (c) 9.7 (d) 9.5
  30. 30.√30 to 1 decimal place? (a) 5.4 (b) 5.5 (c) 5.3 (d) 5.6
  31. 31.Best estimate of 3357 ÷ 63? (a) 56 (b) 560 (c) 5600
  32. 32.Best estimate of 2182 ÷ 88? (a) 240 (b) 2400 (c) 24
  33. 33.Best estimate of 6337 ÷ 88? (a) 7000 (b) 700 (c) 70
  34. 34.√34 to 1 decimal place? (a) 5.8 (b) 5.6 (c) 5.7 (d) 5.5
  35. 35.Best estimate of 718 ÷ 46? (a) 14 (b) 140 (c) 1400
  36. 36.√87 to 1 decimal place? (a) 9.3 (b) 9.6 (c) 9.5 (d) 9.4
  37. 37.√71 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.2 (d) 8.5
  38. 38.Best estimate of 2240 ÷ 76? (a) 280 (b) 28 (c) 2800
  39. 39.√85 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 9.3 (d) 9.2
  40. 40.Best estimate of 1998 ÷ 32? (a) 6700 (b) 67 (c) 670

Answer key

  1. 8.7
  2. 32
  3. 27
  4. 84
  5. 26
  6. 6.9
  7. 33
  8. 9.5
  9. 38
  10. 5.1
  11. 9.6
  12. 4.6
  13. 54
  14. 9.2
  15. 9.4
  16. 6.5
  17. 28
  18. 41
  19. 82
  20. 71
  21. 73
  22. 62
  23. 8.3
  24. 8.1
  25. 89
  26. 67
  27. 36
  28. 92
  29. 9.4
  30. 5.5
  31. 56
  32. 24
  33. 70
  34. 5.8
  35. 14
  36. 9.3
  37. 8.4
  38. 28
  39. 9.2
  40. 67

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