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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 222 · 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.√56 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.5 (d) 7.8
  2. 2.√35 to 1 decimal place? (a) 5.9 (b) 6.2 (c) 6.0 (d) 6.1
  3. 3.√88 to 1 decimal place? (a) 9.6 (b) 9.4 (c) 9.5 (d) 9.7
  4. 4.Best estimate of 2688 ÷ 73? (a) 3800 (b) 38 (c) 380
  5. 5.√92 to 1 decimal place? (a) 9.8 (b) 9.6 (c) 9.7 (d) 9.9
  6. 6.√42 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.3 (d) 6.4
  7. 7.√69 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.3 (d) 8.4
  8. 8.Best estimate of 1348 ÷ 24? (a) 67 (b) 6700 (c) 670
  9. 9.√50 to 1 decimal place? (a) 7.1 (b) 7.3 (c) 7.2 (d) 7.0
  10. 10.Best estimate of 974 ÷ 22? (a) 49 (b) 490 (c) 4900
  11. 11.Best estimate of 1330 ÷ 53? (a) 27 (b) 270 (c) 2700
  12. 12.Best estimate of 1421 ÷ 74? (a) 2000 (b) 200 (c) 20
  13. 13.√76 to 1 decimal place? (a) 8.5 (b) 8.7 (c) 8.8 (d) 8.6
  14. 14.√59 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 7.8 (d) 7.7
  15. 15.Best estimate of 5594 ÷ 72? (a) 80 (b) 800 (c) 8000
  16. 16.√52 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 7.0 (d) 7.3
  17. 17.√55 to 1 decimal place? (a) 7.2 (b) 7.5 (c) 7.4 (d) 7.3
  18. 18.√98 to 1 decimal place? (a) 9.9 (b) 10.1 (c) 10.2 (d) 10.0
  19. 19.√32 to 1 decimal place? (a) 5.6 (b) 5.8 (c) 5.9 (d) 5.7
  20. 20.√23 to 1 decimal place? (a) 5.0 (b) 4.9 (c) 5.1 (d) 4.8
  21. 21.Best estimate of 828 ÷ 62? (a) 1400 (b) 14 (c) 140
  22. 22.Best estimate of 626 ÷ 28? (a) 21 (b) 2100 (c) 210
  23. 23.Best estimate of 847 ÷ 42? (a) 210 (b) 2100 (c) 21
  24. 24.Best estimate of 2917 ÷ 89? (a) 320 (b) 3200 (c) 32
  25. 25.√61 to 1 decimal place? (a) 7.9 (b) 8.1 (c) 7.8 (d) 8.0
  26. 26.Best estimate of 2783 ÷ 73? (a) 400 (b) 40 (c) 4000
  27. 27.√96 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 9.6 (d) 9.9
  28. 28.√80 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.9 (d) 8.8
  29. 29.Best estimate of 1565 ÷ 34? (a) 52 (b) 520 (c) 5200
  30. 30.√94 to 1 decimal place? (a) 9.7 (b) 9.9 (c) 10.0 (d) 9.8
  31. 31.Best estimate of 1934 ÷ 64? (a) 320 (b) 3200 (c) 32
  32. 32.Best estimate of 1658 ÷ 24? (a) 83 (b) 830 (c) 8300
  33. 33.Best estimate of 1513 ÷ 72? (a) 22 (b) 2200 (c) 220
  34. 34.Best estimate of 7064 ÷ 82? (a) 8800 (b) 88 (c) 880
  35. 35.Best estimate of 3064 ÷ 32? (a) 1020 (b) 10200 (c) 102
  36. 36.√51 to 1 decimal place? (a) 7.0 (b) 7.1 (c) 6.9 (d) 7.2
  37. 37.Best estimate of 5749 ÷ 71? (a) 82 (b) 820 (c) 8200
  38. 38.Best estimate of 712 ÷ 54? (a) 140 (b) 14 (c) 1400
  39. 39.Best estimate of 1521 ÷ 74? (a) 22 (b) 2200 (c) 220
  40. 40.√22 to 1 decimal place? (a) 4.7 (b) 4.9 (c) 5.0 (d) 4.8

Answer key

  1. 7.5
  2. 5.9
  3. 9.4
  4. 38
  5. 9.6
  6. 6.5
  7. 8.3
  8. 67
  9. 7.1
  10. 49
  11. 27
  12. 20
  13. 8.7
  14. 7.7
  15. 80
  16. 7.2
  17. 7.4
  18. 9.9
  19. 5.7
  20. 4.8
  21. 14
  22. 21
  23. 21
  24. 32
  25. 7.8
  26. 40
  27. 9.8
  28. 8.9
  29. 52
  30. 9.7
  31. 32
  32. 83
  33. 22
  34. 88
  35. 102
  36. 7.1
  37. 82
  38. 14
  39. 22
  40. 4.7

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