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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 458 · 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.√56 to 1 decimal place? (a) 7.2 (b) 7.5 (c) 7.3 (d) 7.4
  2. 2.√35 to 1 decimal place? (a) 6.0 (b) 5.7 (c) 5.8 (d) 5.9
  3. 3.Best estimate of 4769 ÷ 67? (a) 6800 (b) 680 (c) 68
  4. 4.Best estimate of 1254 ÷ 56? (a) 210 (b) 21 (c) 2100
  5. 5.Best estimate of 1088 ÷ 82? (a) 1400 (b) 140 (c) 14
  6. 6.Best estimate of 1220 ÷ 73? (a) 17 (b) 1700 (c) 170
  7. 7.Best estimate of 1158 ÷ 42? (a) 290 (b) 29 (c) 2900
  8. 8.√61 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 8.1 (d) 7.8
  9. 9.√32 to 1 decimal place? (a) 5.7 (b) 5.5 (c) 5.6 (d) 5.8
  10. 10.√38 to 1 decimal place? (a) 6.3 (b) 6.0 (c) 6.2 (d) 6.1
  11. 11.√40 to 1 decimal place? (a) 6.0 (b) 6.3 (c) 6.1 (d) 6.2
  12. 12.√29 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.4 (d) 5.5
  13. 13.Best estimate of 3530 ÷ 42? (a) 8800 (b) 88 (c) 880
  14. 14.Best estimate of 6252 ÷ 83? (a) 780 (b) 7800 (c) 78
  15. 15.Best estimate of 729 ÷ 52? (a) 15 (b) 150 (c) 1500
  16. 16.Best estimate of 3514 ÷ 56? (a) 59 (b) 5900 (c) 590
  17. 17.√62 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 7.7 (d) 8.0
  18. 18.√70 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.4 (d) 8.1
  19. 19.Best estimate of 1074 ÷ 22? (a) 54 (b) 540 (c) 5400
  20. 20.√21 to 1 decimal place? (a) 4.9 (b) 4.6 (c) 4.8 (d) 4.7
  21. 21.Best estimate of 2185 ÷ 68? (a) 310 (b) 31 (c) 3100
  22. 22.√51 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 7.2 (d) 7.3
  23. 23.Best estimate of 2287 ÷ 48? (a) 460 (b) 4600 (c) 46
  24. 24.Best estimate of 4191 ÷ 81? (a) 520 (b) 52 (c) 5200
  25. 25.√79 to 1 decimal place? (a) 8.7 (b) 8.9 (c) 8.8 (d) 8.6
  26. 26.Best estimate of 623 ÷ 36? (a) 16 (b) 160 (c) 1600
  27. 27.Best estimate of 2074 ÷ 32? (a) 69 (b) 6900 (c) 690
  28. 28.Best estimate of 2790 ÷ 87? (a) 31 (b) 310 (c) 3100
  29. 29.Best estimate of 406 ÷ 21? (a) 200 (b) 2000 (c) 20
  30. 30.Best estimate of 2257 ÷ 78? (a) 2800 (b) 280 (c) 28
  31. 31.√87 to 1 decimal place? (a) 9.4 (b) 9.2 (c) 9.1 (d) 9.3
  32. 32.√52 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.1 (d) 7.2
  33. 33.Best estimate of 3547 ÷ 56? (a) 5900 (b) 59 (c) 590
  34. 34.Best estimate of 4284 ÷ 61? (a) 71 (b) 7100 (c) 710
  35. 35.Best estimate of 1627 ÷ 32? (a) 540 (b) 54 (c) 5400
  36. 36.Best estimate of 7656 ÷ 83? (a) 9600 (b) 96 (c) 960
  37. 37.Best estimate of 2342 ÷ 26? (a) 78 (b) 7800 (c) 780
  38. 38.Best estimate of 5895 ÷ 64? (a) 980 (b) 98 (c) 9800
  39. 39.√94 to 1 decimal place? (a) 10.0 (b) 9.8 (c) 9.9 (d) 9.7
  40. 40.√72 to 1 decimal place? (a) 8.4 (b) 8.7 (c) 8.5 (d) 8.6

Answer key

  1. 7.5
  2. 5.9
  3. 68
  4. 21
  5. 14
  6. 17
  7. 29
  8. 7.8
  9. 5.7
  10. 6.2
  11. 6.3
  12. 5.4
  13. 88
  14. 78
  15. 15
  16. 59
  17. 7.9
  18. 8.4
  19. 54
  20. 4.6
  21. 31
  22. 7.1
  23. 46
  24. 52
  25. 8.9
  26. 16
  27. 69
  28. 31
  29. 20
  30. 28
  31. 9.3
  32. 7.2
  33. 59
  34. 71
  35. 54
  36. 96
  37. 78
  38. 98
  39. 9.7
  40. 8.5

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