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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 356 · 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.√42 to 1 decimal place? (a) 6.6 (b) 6.3 (c) 6.4 (d) 6.5
  2. 2.Best estimate of 1695 ÷ 72? (a) 240 (b) 24 (c) 2400
  3. 3.Best estimate of 641 ÷ 48? (a) 130 (b) 1300 (c) 13
  4. 4.√22 to 1 decimal place? (a) 4.6 (b) 4.7 (c) 4.5 (d) 4.4
  5. 5.Best estimate of 8332 ÷ 88? (a) 930 (b) 93 (c) 9300
  6. 6.Best estimate of 1869 ÷ 57? (a) 31 (b) 310 (c) 3100
  7. 7.√61 to 1 decimal place? (a) 7.6 (b) 7.8 (c) 7.5 (d) 7.7
  8. 8.√58 to 1 decimal place? (a) 7.5 (b) 7.7 (c) 7.8 (d) 7.6
  9. 9.√74 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.5 (d) 8.7
  10. 10.√26 to 1 decimal place? (a) 5.4 (b) 5.1 (c) 5.3 (d) 5.2
  11. 11.√41 to 1 decimal place? (a) 6.4 (b) 6.3 (c) 6.2 (d) 6.5
  12. 12.√79 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 8.8 (d) 8.7
  13. 13.Best estimate of 3459 ÷ 42? (a) 86 (b) 860 (c) 8600
  14. 14.Best estimate of 5101 ÷ 61? (a) 85 (b) 850 (c) 8500
  15. 15.√96 to 1 decimal place? (a) 9.8 (b) 10.0 (c) 10.1 (d) 9.9
  16. 16.Best estimate of 1331 ÷ 27? (a) 4400 (b) 440 (c) 44
  17. 17.Best estimate of 4819 ÷ 82? (a) 600 (b) 6000 (c) 60
  18. 18.Best estimate of 3676 ÷ 67? (a) 530 (b) 5300 (c) 53
  19. 19.Best estimate of 5276 ÷ 77? (a) 6600 (b) 66 (c) 660
  20. 20.Best estimate of 759 ÷ 52? (a) 1500 (b) 150 (c) 15
  21. 21.Best estimate of 1570 ÷ 32? (a) 5200 (b) 520 (c) 52
  22. 22.√55 to 1 decimal place? (a) 7.2 (b) 7.5 (c) 7.4 (d) 7.3
  23. 23.Best estimate of 1310 ÷ 81? (a) 16 (b) 1600 (c) 160
  24. 24.Best estimate of 365 ÷ 27? (a) 1200 (b) 120 (c) 12
  25. 25.Best estimate of 536 ÷ 34? (a) 1800 (b) 18 (c) 180
  26. 26.√31 to 1 decimal place? (a) 5.5 (b) 5.6 (c) 5.4 (d) 5.7
  27. 27.√59 to 1 decimal place? (a) 7.8 (b) 7.5 (c) 7.7 (d) 7.6
  28. 28.√71 to 1 decimal place? (a) 8.4 (b) 8.2 (c) 8.3 (d) 8.1
  29. 29.Best estimate of 3160 ÷ 33? (a) 10500 (b) 1050 (c) 105
  30. 30.Best estimate of 1699 ÷ 32? (a) 5700 (b) 570 (c) 57
  31. 31.Best estimate of 3440 ÷ 38? (a) 860 (b) 86 (c) 8600
  32. 32.Best estimate of 2165 ÷ 89? (a) 2400 (b) 24 (c) 240
  33. 33.Best estimate of 1416 ÷ 56? (a) 24 (b) 240 (c) 2400
  34. 34.√28 to 1 decimal place? (a) 5.2 (b) 5.4 (c) 5.3 (d) 5.5
  35. 35.Best estimate of 1616 ÷ 47? (a) 320 (b) 32 (c) 3200
  36. 36.Best estimate of 3830 ÷ 72? (a) 550 (b) 55 (c) 5500
  37. 37.√84 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 9.4 (d) 9.3
  38. 38.√76 to 1 decimal place? (a) 8.9 (b) 8.7 (c) 8.8 (d) 9.0
  39. 39.Best estimate of 600 ÷ 24? (a) 300 (b) 30 (c) 3000
  40. 40.√46 to 1 decimal place? (a) 6.8 (b) 7.1 (c) 6.9 (d) 7.0

Answer key

  1. 6.5
  2. 24
  3. 13
  4. 4.7
  5. 93
  6. 31
  7. 7.8
  8. 7.6
  9. 8.6
  10. 5.1
  11. 6.4
  12. 8.9
  13. 86
  14. 85
  15. 9.8
  16. 44
  17. 60
  18. 53
  19. 66
  20. 15
  21. 52
  22. 7.4
  23. 16
  24. 12
  25. 18
  26. 5.6
  27. 7.7
  28. 8.4
  29. 105
  30. 57
  31. 86
  32. 24
  33. 24
  34. 5.3
  35. 32
  36. 55
  37. 9.2
  38. 8.7
  39. 30
  40. 6.8

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