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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 417 · 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.√85 to 1 decimal place? (a) 9.1 (b) 8.9 (c) 9.2 (d) 9.0
  2. 2.Best estimate of 5626 ÷ 79? (a) 700 (b) 7000 (c) 70
  3. 3.√26 to 1 decimal place? (a) 5.2 (b) 5.3 (c) 5.1 (d) 5.4
  4. 4.Best estimate of 2094 ÷ 72? (a) 30 (b) 3000 (c) 300
  5. 5.√66 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.4 (d) 8.3
  6. 6.Best estimate of 1271 ÷ 56? (a) 210 (b) 21 (c) 2100
  7. 7.√88 to 1 decimal place? (a) 9.5 (b) 9.3 (c) 9.4 (d) 9.6
  8. 8.√30 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.4 (d) 5.5
  9. 9.Best estimate of 3720 ÷ 77? (a) 470 (b) 4700 (c) 47
  10. 10.Best estimate of 4310 ÷ 81? (a) 5400 (b) 54 (c) 540
  11. 11.√62 to 1 decimal place? (a) 8.0 (b) 7.8 (c) 7.9 (d) 7.7
  12. 12.Best estimate of 7343 ÷ 77? (a) 92 (b) 920 (c) 9200
  13. 13.Best estimate of 3417 ÷ 56? (a) 5700 (b) 570 (c) 57
  14. 14.Best estimate of 1761 ÷ 56? (a) 290 (b) 29 (c) 2900
  15. 15.Best estimate of 1095 ÷ 32? (a) 3700 (b) 37 (c) 370
  16. 16.Best estimate of 1137 ÷ 31? (a) 380 (b) 38 (c) 3800
  17. 17.√90 to 1 decimal place? (a) 9.6 (b) 9.4 (c) 9.7 (d) 9.5
  18. 18.√65 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 7.9 (d) 8.0
  19. 19.Best estimate of 1412 ÷ 27? (a) 470 (b) 47 (c) 4700
  20. 20.Best estimate of 1050 ÷ 27? (a) 3500 (b) 350 (c) 35
  21. 21.Best estimate of 711 ÷ 37? (a) 1800 (b) 180 (c) 18
  22. 22.Best estimate of 5346 ÷ 86? (a) 590 (b) 59 (c) 5900
  23. 23.√37 to 1 decimal place? (a) 5.8 (b) 6.1 (c) 5.9 (d) 6.0
  24. 24.√46 to 1 decimal place? (a) 7.0 (b) 6.7 (c) 6.8 (d) 6.9
  25. 25.√41 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.4 (d) 6.5
  26. 26.Best estimate of 971 ÷ 36? (a) 2400 (b) 24 (c) 240
  27. 27.√87 to 1 decimal place? (a) 9.4 (b) 9.2 (c) 9.5 (d) 9.3
  28. 28.Best estimate of 5028 ÷ 84? (a) 630 (b) 63 (c) 6300
  29. 29.√22 to 1 decimal place? (a) 4.8 (b) 4.7 (c) 5.0 (d) 4.9
  30. 30.√40 to 1 decimal place? (a) 6.1 (b) 6.3 (c) 6.4 (d) 6.2
  31. 31.√43 to 1 decimal place? (a) 6.9 (b) 6.6 (c) 6.8 (d) 6.7
  32. 32.√61 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 8.0 (d) 7.9
  33. 33.Best estimate of 6036 ÷ 88? (a) 6700 (b) 670 (c) 67
  34. 34.Best estimate of 991 ÷ 53? (a) 20 (b) 200 (c) 2000
  35. 35.Best estimate of 1866 ÷ 34? (a) 620 (b) 6200 (c) 62
  36. 36.Best estimate of 770 ÷ 27? (a) 2600 (b) 260 (c) 26
  37. 37.Best estimate of 1234 ÷ 52? (a) 250 (b) 2500 (c) 25
  38. 38.Best estimate of 2458 ÷ 38? (a) 610 (b) 6100 (c) 61
  39. 39.Best estimate of 2846 ÷ 76? (a) 360 (b) 36 (c) 3600
  40. 40.Best estimate of 1152 ÷ 42? (a) 2900 (b) 290 (c) 29

Answer key

  1. 9.2
  2. 70
  3. 5.1
  4. 30
  5. 8.1
  6. 21
  7. 9.4
  8. 5.5
  9. 47
  10. 54
  11. 7.9
  12. 92
  13. 57
  14. 29
  15. 37
  16. 38
  17. 9.5
  18. 8.1
  19. 47
  20. 35
  21. 18
  22. 59
  23. 6.1
  24. 6.8
  25. 6.4
  26. 24
  27. 9.3
  28. 63
  29. 4.7
  30. 6.3
  31. 6.6
  32. 7.8
  33. 67
  34. 20
  35. 62
  36. 26
  37. 25
  38. 61
  39. 36
  40. 29

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