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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 836 · 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.√24 to 1 decimal place? (a) 4.8 (b) 5.1 (c) 4.9 (d) 5.0
  2. 2.√21 to 1 decimal place? (a) 4.8 (b) 4.9 (c) 4.6 (d) 4.7
  3. 3.√42 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.7 (d) 6.4
  4. 4.Best estimate of 6125 ÷ 87? (a) 68 (b) 680 (c) 6800
  5. 5.Best estimate of 2120 ÷ 49? (a) 420 (b) 4200 (c) 42
  6. 6.Best estimate of 604 ÷ 34? (a) 20 (b) 200 (c) 2000
  7. 7.√34 to 1 decimal place? (a) 6.0 (b) 5.8 (c) 5.7 (d) 5.9
  8. 8.√84 to 1 decimal place? (a) 9.1 (b) 9.3 (c) 9.2 (d) 9.4
  9. 9.Best estimate of 896 ÷ 63? (a) 1500 (b) 15 (c) 150
  10. 10.√38 to 1 decimal place? (a) 6.3 (b) 6.2 (c) 6.5 (d) 6.4
  11. 11.√30 to 1 decimal place? (a) 5.7 (b) 5.8 (c) 5.6 (d) 5.5
  12. 12.Best estimate of 2425 ÷ 62? (a) 4000 (b) 40 (c) 400
  13. 13.Best estimate of 1438 ÷ 68? (a) 210 (b) 21 (c) 2100
  14. 14.Best estimate of 2035 ÷ 52? (a) 4100 (b) 410 (c) 41
  15. 15.Best estimate of 2365 ÷ 41? (a) 590 (b) 5900 (c) 59
  16. 16.√32 to 1 decimal place? (a) 5.6 (b) 5.9 (c) 5.7 (d) 5.8
  17. 17.Best estimate of 4624 ÷ 87? (a) 510 (b) 5100 (c) 51
  18. 18.Best estimate of 2866 ÷ 74? (a) 4100 (b) 41 (c) 410
  19. 19.√37 to 1 decimal place? (a) 6.4 (b) 6.3 (c) 6.1 (d) 6.2
  20. 20.Best estimate of 1491 ÷ 42? (a) 37 (b) 370 (c) 3700
  21. 21.√35 to 1 decimal place? (a) 6.1 (b) 5.9 (c) 6.0 (d) 5.8
  22. 22.Best estimate of 1265 ÷ 71? (a) 1800 (b) 18 (c) 180
  23. 23.√31 to 1 decimal place? (a) 5.4 (b) 5.5 (c) 5.6 (d) 5.7
  24. 24.√23 to 1 decimal place? (a) 5.1 (b) 4.9 (c) 4.8 (d) 5.0
  25. 25.√65 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 8.2 (d) 8.3
  26. 26.√92 to 1 decimal place? (a) 9.9 (b) 9.6 (c) 9.7 (d) 9.8
  27. 27.Best estimate of 1978 ÷ 71? (a) 280 (b) 2800 (c) 28
  28. 28.Best estimate of 1430 ÷ 48? (a) 290 (b) 2900 (c) 29
  29. 29.√58 to 1 decimal place? (a) 7.7 (b) 7.5 (c) 7.6 (d) 7.8
  30. 30.Best estimate of 3215 ÷ 48? (a) 6400 (b) 640 (c) 64
  31. 31.Best estimate of 5240 ÷ 57? (a) 87 (b) 8700 (c) 870
  32. 32.Best estimate of 7818 ÷ 83? (a) 9800 (b) 98 (c) 980
  33. 33.√28 to 1 decimal place? (a) 5.1 (b) 5.2 (c) 5.3 (d) 5.4
  34. 34.Best estimate of 864 ÷ 21? (a) 4300 (b) 43 (c) 430
  35. 35.√79 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 8.9 (d) 9.0
  36. 36.Best estimate of 1030 ÷ 34? (a) 34 (b) 3400 (c) 340
  37. 37.Best estimate of 996 ÷ 69? (a) 140 (b) 14 (c) 1400
  38. 38.Best estimate of 7484 ÷ 84? (a) 940 (b) 94 (c) 9400
  39. 39.√40 to 1 decimal place? (a) 6.5 (b) 6.3 (c) 6.6 (d) 6.4
  40. 40.√75 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.8 (d) 8.9

Answer key

  1. 4.9
  2. 4.6
  3. 6.5
  4. 68
  5. 42
  6. 20
  7. 5.8
  8. 9.2
  9. 15
  10. 6.2
  11. 5.5
  12. 40
  13. 21
  14. 41
  15. 59
  16. 5.7
  17. 51
  18. 41
  19. 6.1
  20. 37
  21. 5.9
  22. 18
  23. 5.6
  24. 4.8
  25. 8.1
  26. 9.6
  27. 28
  28. 29
  29. 7.6
  30. 64
  31. 87
  32. 98
  33. 5.3
  34. 43
  35. 8.9
  36. 34
  37. 14
  38. 94
  39. 6.3
  40. 8.7

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