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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 605 · 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.√47 to 1 decimal place? (a) 6.9 (b) 7.1 (c) 7.0 (d) 6.8
  2. 2.Best estimate of 4644 ÷ 86? (a) 520 (b) 5200 (c) 52
  3. 3.Best estimate of 795 ÷ 39? (a) 2000 (b) 20 (c) 200
  4. 4.Best estimate of 2914 ÷ 38? (a) 73 (b) 730 (c) 7300
  5. 5.Best estimate of 2276 ÷ 88? (a) 25 (b) 2500 (c) 250
  6. 6.√58 to 1 decimal place? (a) 7.9 (b) 7.7 (c) 7.8 (d) 7.6
  7. 7.Best estimate of 6817 ÷ 83? (a) 8500 (b) 850 (c) 85
  8. 8.√34 to 1 decimal place? (a) 5.9 (b) 6.1 (c) 5.8 (d) 6.0
  9. 9.Best estimate of 1964 ÷ 43? (a) 490 (b) 4900 (c) 49
  10. 10.√48 to 1 decimal place? (a) 7.2 (b) 6.9 (c) 7.1 (d) 7.0
  11. 11.√74 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.5 (d) 8.8
  12. 12.√55 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.5 (d) 7.6
  13. 13.Best estimate of 5942 ÷ 71? (a) 850 (b) 85 (c) 8500
  14. 14.√40 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.5 (d) 6.4
  15. 15.Best estimate of 2145 ÷ 27? (a) 72 (b) 7200 (c) 720
  16. 16.Best estimate of 5217 ÷ 57? (a) 870 (b) 87 (c) 8700
  17. 17.Best estimate of 3125 ÷ 38? (a) 78 (b) 7800 (c) 780
  18. 18.√26 to 1 decimal place? (a) 5.1 (b) 5.4 (c) 5.3 (d) 5.2
  19. 19.√29 to 1 decimal place? (a) 5.4 (b) 5.5 (c) 5.6 (d) 5.3
  20. 20.√65 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 7.9 (d) 8.2
  21. 21.Best estimate of 3592 ÷ 51? (a) 720 (b) 7200 (c) 72
  22. 22.Best estimate of 2767 ÷ 42? (a) 6900 (b) 69 (c) 690
  23. 23.Best estimate of 684 ÷ 36? (a) 17 (b) 170 (c) 1700
  24. 24.√43 to 1 decimal place? (a) 6.9 (b) 6.8 (c) 6.7 (d) 6.6
  25. 25.Best estimate of 2027 ÷ 24? (a) 1010 (b) 10100 (c) 101
  26. 26.Best estimate of 333 ÷ 22? (a) 170 (b) 1700 (c) 17
  27. 27.Best estimate of 1543 ÷ 48? (a) 310 (b) 3100 (c) 31
  28. 28.√94 to 1 decimal place? (a) 9.6 (b) 9.9 (c) 9.8 (d) 9.7
  29. 29.√61 to 1 decimal place? (a) 8.0 (b) 7.9 (c) 8.1 (d) 7.8
  30. 30.Best estimate of 3206 ÷ 77? (a) 4000 (b) 40 (c) 400
  31. 31.Best estimate of 1712 ÷ 28? (a) 570 (b) 57 (c) 5700
  32. 32.Best estimate of 2270 ÷ 36? (a) 570 (b) 5700 (c) 57
  33. 33.√67 to 1 decimal place? (a) 8.4 (b) 8.2 (c) 8.1 (d) 8.3
  34. 34.Best estimate of 2062 ÷ 56? (a) 3400 (b) 340 (c) 34
  35. 35.Best estimate of 2480 ÷ 34? (a) 830 (b) 83 (c) 8300
  36. 36.Best estimate of 3425 ÷ 64? (a) 570 (b) 57 (c) 5700
  37. 37.√44 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.9 (d) 6.8
  38. 38.Best estimate of 4125 ÷ 52? (a) 83 (b) 8300 (c) 830
  39. 39.Best estimate of 2133 ÷ 53? (a) 43 (b) 4300 (c) 430
  40. 40.√72 to 1 decimal place? (a) 8.5 (b) 8.3 (c) 8.4 (d) 8.6

Answer key

  1. 6.9
  2. 52
  3. 20
  4. 73
  5. 25
  6. 7.6
  7. 85
  8. 5.8
  9. 49
  10. 6.9
  11. 8.6
  12. 7.4
  13. 85
  14. 6.3
  15. 72
  16. 87
  17. 78
  18. 5.1
  19. 5.4
  20. 8.1
  21. 72
  22. 69
  23. 17
  24. 6.6
  25. 101
  26. 17
  27. 31
  28. 9.7
  29. 7.8
  30. 40
  31. 57
  32. 57
  33. 8.2
  34. 34
  35. 83
  36. 57
  37. 6.6
  38. 83
  39. 43
  40. 8.5

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