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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 373 · 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.√96 to 1 decimal place? (a) 9.7 (b) 9.9 (c) 10.0 (d) 9.8
  2. 2.√37 to 1 decimal place? (a) 6.3 (b) 6.1 (c) 6.4 (d) 6.2
  3. 3.√85 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.5 (d) 9.3
  4. 4.√56 to 1 decimal place? (a) 7.5 (b) 7.3 (c) 7.6 (d) 7.4
  5. 5.Best estimate of 5831 ÷ 71? (a) 830 (b) 8300 (c) 83
  6. 6.Best estimate of 3111 ÷ 49? (a) 62 (b) 6200 (c) 620
  7. 7.Best estimate of 3725 ÷ 52? (a) 7500 (b) 75 (c) 750
  8. 8.√50 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 7.1 (d) 6.8
  9. 9.Best estimate of 1399 ÷ 76? (a) 17 (b) 1700 (c) 170
  10. 10.√94 to 1 decimal place? (a) 9.6 (b) 9.8 (c) 9.7 (d) 9.5
  11. 11.√69 to 1 decimal place? (a) 8.6 (b) 8.3 (c) 8.4 (d) 8.5
  12. 12.√53 to 1 decimal place? (a) 7.0 (b) 7.3 (c) 7.1 (d) 7.2
  13. 13.√59 to 1 decimal place? (a) 7.7 (b) 7.5 (c) 7.6 (d) 7.8
  14. 14.Best estimate of 1772 ÷ 23? (a) 8900 (b) 890 (c) 89
  15. 15.Best estimate of 1349 ÷ 64? (a) 220 (b) 2200 (c) 22
  16. 16.Best estimate of 2790 ÷ 37? (a) 70 (b) 700 (c) 7000
  17. 17.√88 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.1 (d) 9.4
  18. 18.Best estimate of 1421 ÷ 26? (a) 4700 (b) 470 (c) 47
  19. 19.√23 to 1 decimal place? (a) 5.0 (b) 4.9 (c) 4.8 (d) 5.1
  20. 20.√27 to 1 decimal place? (a) 5.2 (b) 5.5 (c) 5.3 (d) 5.4
  21. 21.Best estimate of 1618 ÷ 56? (a) 270 (b) 27 (c) 2700
  22. 22.Best estimate of 1285 ÷ 39? (a) 32 (b) 320 (c) 3200
  23. 23.√40 to 1 decimal place? (a) 6.1 (b) 6.4 (c) 6.3 (d) 6.2
  24. 24.√32 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.4 (d) 5.5
  25. 25.√80 to 1 decimal place? (a) 8.8 (b) 9.0 (c) 8.9 (d) 8.7
  26. 26.Best estimate of 4144 ÷ 82? (a) 520 (b) 52 (c) 5200
  27. 27.Best estimate of 1784 ÷ 44? (a) 450 (b) 45 (c) 4500
  28. 28.√55 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.3 (d) 7.2
  29. 29.√42 to 1 decimal place? (a) 6.4 (b) 6.6 (c) 6.7 (d) 6.5
  30. 30.Best estimate of 3908 ÷ 62? (a) 650 (b) 65 (c) 6500
  31. 31.Best estimate of 1767 ÷ 52? (a) 350 (b) 35 (c) 3500
  32. 32.√61 to 1 decimal place? (a) 7.7 (b) 7.5 (c) 7.8 (d) 7.6
  33. 33.√29 to 1 decimal place? (a) 5.4 (b) 5.5 (c) 5.7 (d) 5.6
  34. 34.√82 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 8.9 (d) 8.8
  35. 35.Best estimate of 2094 ÷ 62? (a) 3500 (b) 350 (c) 35
  36. 36.√34 to 1 decimal place? (a) 5.9 (b) 5.6 (c) 5.7 (d) 5.8
  37. 37.√26 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.1 (d) 5.4
  38. 38.Best estimate of 1296 ÷ 41? (a) 3200 (b) 32 (c) 320
  39. 39.√66 to 1 decimal place? (a) 7.8 (b) 8.0 (c) 8.1 (d) 7.9
  40. 40.Best estimate of 1016 ÷ 28? (a) 340 (b) 3400 (c) 34

Answer key

  1. 9.8
  2. 6.1
  3. 9.2
  4. 7.5
  5. 83
  6. 62
  7. 75
  8. 7.1
  9. 17
  10. 9.7
  11. 8.3
  12. 7.3
  13. 7.7
  14. 89
  15. 22
  16. 70
  17. 9.4
  18. 47
  19. 4.8
  20. 5.2
  21. 27
  22. 32
  23. 6.3
  24. 5.7
  25. 8.9
  26. 52
  27. 45
  28. 7.4
  29. 6.5
  30. 65
  31. 35
  32. 7.8
  33. 5.4
  34. 9.1
  35. 35
  36. 5.8
  37. 5.1
  38. 32
  39. 8.1
  40. 34

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