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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 734 · 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.√41 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.3 (d) 6.1
  2. 2.Best estimate of 2326 ÷ 32? (a) 7800 (b) 780 (c) 78
  3. 3.Best estimate of 4605 ÷ 66? (a) 6600 (b) 660 (c) 66
  4. 4.Best estimate of 3024 ÷ 58? (a) 500 (b) 5000 (c) 50
  5. 5.√94 to 1 decimal place? (a) 9.9 (b) 9.6 (c) 9.7 (d) 9.8
  6. 6.√50 to 1 decimal place? (a) 6.9 (b) 7.1 (c) 6.8 (d) 7.0
  7. 7.√38 to 1 decimal place? (a) 6.1 (b) 5.9 (c) 6.2 (d) 6.0
  8. 8.√31 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.6 (d) 5.7
  9. 9.√26 to 1 decimal place? (a) 5.1 (b) 5.3 (c) 5.0 (d) 5.2
  10. 10.Best estimate of 1212 ÷ 48? (a) 240 (b) 24 (c) 2400
  11. 11.Best estimate of 3145 ÷ 87? (a) 350 (b) 35 (c) 3500
  12. 12.√53 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.1 (d) 7.2
  13. 13.Best estimate of 2779 ÷ 39? (a) 69 (b) 6900 (c) 690
  14. 14.Best estimate of 1707 ÷ 27? (a) 570 (b) 5700 (c) 57
  15. 15.Best estimate of 1763 ÷ 56? (a) 290 (b) 29 (c) 2900
  16. 16.Best estimate of 6958 ÷ 79? (a) 87 (b) 870 (c) 8700
  17. 17.Best estimate of 4797 ÷ 59? (a) 80 (b) 800 (c) 8000
  18. 18.Best estimate of 6321 ÷ 77? (a) 7900 (b) 79 (c) 790
  19. 19.Best estimate of 2316 ÷ 49? (a) 46 (b) 460 (c) 4600
  20. 20.Best estimate of 1717 ÷ 73? (a) 2500 (b) 250 (c) 25
  21. 21.√47 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.9 (d) 6.6
  22. 22.Best estimate of 366 ÷ 27? (a) 12 (b) 120 (c) 1200
  23. 23.Best estimate of 2381 ÷ 64? (a) 40 (b) 4000 (c) 400
  24. 24.Best estimate of 1691 ÷ 72? (a) 24 (b) 2400 (c) 240
  25. 25.√98 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.9 (d) 9.8
  26. 26.√40 to 1 decimal place? (a) 6.1 (b) 6.3 (c) 6.2 (d) 6.0
  27. 27.Best estimate of 706 ÷ 42? (a) 18 (b) 1800 (c) 180
  28. 28.√55 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.3 (d) 7.6
  29. 29.√92 to 1 decimal place? (a) 9.9 (b) 9.6 (c) 9.7 (d) 9.8
  30. 30.Best estimate of 1037 ÷ 32? (a) 350 (b) 35 (c) 3500
  31. 31.√83 to 1 decimal place? (a) 9.1 (b) 8.9 (c) 9.0 (d) 9.2
  32. 32.√28 to 1 decimal place? (a) 5.3 (b) 5.0 (c) 5.2 (d) 5.1
  33. 33.√48 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 6.8 (d) 7.1
  34. 34.Best estimate of 1877 ÷ 26? (a) 63 (b) 630 (c) 6300
  35. 35.Best estimate of 2048 ÷ 52? (a) 4100 (b) 41 (c) 410
  36. 36.√27 to 1 decimal place? (a) 5.2 (b) 5.3 (c) 5.1 (d) 5.4
  37. 37.Best estimate of 2136 ÷ 26? (a) 710 (b) 7100 (c) 71
  38. 38.√66 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.1 (d) 8.2
  39. 39.Best estimate of 3004 ÷ 32? (a) 100 (b) 1000 (c) 10000
  40. 40.Best estimate of 4649 ÷ 76? (a) 5800 (b) 580 (c) 58

Answer key

  1. 6.4
  2. 78
  3. 66
  4. 50
  5. 9.7
  6. 7.1
  7. 6.2
  8. 5.6
  9. 5.1
  10. 24
  11. 35
  12. 7.3
  13. 69
  14. 57
  15. 29
  16. 87
  17. 80
  18. 79
  19. 46
  20. 25
  21. 6.9
  22. 12
  23. 40
  24. 24
  25. 9.9
  26. 6.3
  27. 18
  28. 7.4
  29. 9.6
  30. 35
  31. 9.1
  32. 5.3
  33. 6.9
  34. 63
  35. 41
  36. 5.2
  37. 71
  38. 8.1
  39. 100
  40. 58

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