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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 440 · 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.√23 to 1 decimal place? (a) 5.0 (b) 4.8 (c) 4.9 (d) 4.7
  2. 2.√40 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.3 (d) 6.4
  3. 3.Best estimate of 2197 ÷ 54? (a) 440 (b) 44 (c) 4400
  4. 4.√20 to 1 decimal place? (a) 4.5 (b) 4.2 (c) 4.4 (d) 4.3
  5. 5.Best estimate of 1205 ÷ 32? (a) 400 (b) 4000 (c) 40
  6. 6.Best estimate of 6625 ÷ 86? (a) 740 (b) 74 (c) 7400
  7. 7.Best estimate of 1514 ÷ 38? (a) 3800 (b) 380 (c) 38
  8. 8.√84 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 8.9 (d) 9.2
  9. 9.√50 to 1 decimal place? (a) 7.0 (b) 7.2 (c) 7.3 (d) 7.1
  10. 10.√31 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 5.7 (d) 5.6
  11. 11.Best estimate of 2829 ÷ 46? (a) 570 (b) 5700 (c) 57
  12. 12.√85 to 1 decimal place? (a) 9.5 (b) 9.3 (c) 9.4 (d) 9.2
  13. 13.Best estimate of 1419 ÷ 38? (a) 350 (b) 3500 (c) 35
  14. 14.√26 to 1 decimal place? (a) 5.0 (b) 4.9 (c) 5.1 (d) 5.2
  15. 15.Best estimate of 3600 ÷ 69? (a) 510 (b) 5100 (c) 51
  16. 16.Best estimate of 798 ÷ 57? (a) 130 (b) 13 (c) 1300
  17. 17.√30 to 1 decimal place? (a) 5.3 (b) 5.5 (c) 5.4 (d) 5.2
  18. 18.√96 to 1 decimal place? (a) 9.9 (b) 10.0 (c) 10.1 (d) 9.8
  19. 19.Best estimate of 1316 ÷ 36? (a) 330 (b) 3300 (c) 33
  20. 20.√32 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.7 (d) 5.6
  21. 21.√38 to 1 decimal place? (a) 6.2 (b) 6.5 (c) 6.4 (d) 6.3
  22. 22.√41 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.1 (d) 6.4
  23. 23.Best estimate of 1121 ÷ 24? (a) 5600 (b) 56 (c) 560
  24. 24.Best estimate of 1070 ÷ 68? (a) 1500 (b) 150 (c) 15
  25. 25.√45 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.7 (d) 6.4
  26. 26.√51 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 6.9 (d) 7.2
  27. 27.√46 to 1 decimal place? (a) 6.7 (b) 6.9 (c) 7.0 (d) 6.8
  28. 28.Best estimate of 5378 ÷ 64? (a) 900 (b) 90 (c) 9000
  29. 29.Best estimate of 4233 ÷ 52? (a) 85 (b) 8500 (c) 850
  30. 30.Best estimate of 798 ÷ 54? (a) 160 (b) 16 (c) 1600
  31. 31.Best estimate of 3641 ÷ 38? (a) 9100 (b) 91 (c) 910
  32. 32.Best estimate of 4340 ÷ 73? (a) 620 (b) 62 (c) 6200
  33. 33.Best estimate of 1953 ÷ 26? (a) 6500 (b) 65 (c) 650
  34. 34.Best estimate of 680 ÷ 53? (a) 14 (b) 1400 (c) 140
  35. 35.√22 to 1 decimal place? (a) 5.0 (b) 4.8 (c) 4.9 (d) 4.7
  36. 36.Best estimate of 806 ÷ 44? (a) 200 (b) 20 (c) 2000
  37. 37.√34 to 1 decimal place? (a) 6.1 (b) 5.8 (c) 5.9 (d) 6.0
  38. 38.Best estimate of 3609 ÷ 64? (a) 6000 (b) 600 (c) 60
  39. 39.Best estimate of 4583 ÷ 86? (a) 5100 (b) 510 (c) 51
  40. 40.Best estimate of 1719 ÷ 71? (a) 25 (b) 250 (c) 2500

Answer key

  1. 4.8
  2. 6.3
  3. 44
  4. 4.5
  5. 40
  6. 74
  7. 38
  8. 9.2
  9. 7.1
  10. 5.6
  11. 57
  12. 9.2
  13. 35
  14. 5.1
  15. 51
  16. 13
  17. 5.5
  18. 9.8
  19. 33
  20. 5.7
  21. 6.2
  22. 6.4
  23. 56
  24. 15
  25. 6.7
  26. 7.1
  27. 6.8
  28. 90
  29. 85
  30. 16
  31. 91
  32. 62
  33. 65
  34. 14
  35. 4.7
  36. 20
  37. 5.8
  38. 60
  39. 51
  40. 25

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