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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 57 · 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.Best estimate of 4707 ÷ 54? (a) 940 (b) 9400 (c) 94
  2. 2.Best estimate of 1784 ÷ 34? (a) 590 (b) 5900 (c) 59
  3. 3.√20 to 1 decimal place? (a) 4.5 (b) 4.6 (c) 4.4 (d) 4.3
  4. 4.Best estimate of 6373 ÷ 82? (a) 800 (b) 8000 (c) 80
  5. 5.Best estimate of 2193 ÷ 76? (a) 27 (b) 2700 (c) 270
  6. 6.√46 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 6.7 (d) 7.0
  7. 7.Best estimate of 894 ÷ 52? (a) 180 (b) 18 (c) 1800
  8. 8.√53 to 1 decimal place? (a) 7.0 (b) 7.2 (c) 7.3 (d) 7.1
  9. 9.Best estimate of 2638 ÷ 86? (a) 290 (b) 29 (c) 2900
  10. 10.Best estimate of 627 ÷ 24? (a) 31 (b) 3100 (c) 310
  11. 11.Best estimate of 3494 ÷ 52? (a) 7000 (b) 700 (c) 70
  12. 12.√26 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.0 (d) 5.1
  13. 13.√42 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.5 (d) 6.6
  14. 14.Best estimate of 1502 ÷ 33? (a) 50 (b) 5000 (c) 500
  15. 15.Best estimate of 6458 ÷ 74? (a) 920 (b) 92 (c) 9200
  16. 16.√40 to 1 decimal place? (a) 6.1 (b) 6.3 (c) 6.2 (d) 6.0
  17. 17.√66 to 1 decimal place? (a) 8.4 (b) 8.2 (c) 8.3 (d) 8.1
  18. 18.√21 to 1 decimal place? (a) 4.4 (b) 4.3 (c) 4.6 (d) 4.5
  19. 19.Best estimate of 2920 ÷ 34? (a) 97 (b) 970 (c) 9700
  20. 20.√37 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 6.0 (d) 6.3
  21. 21.√77 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.7 (d) 9.0
  22. 22.Best estimate of 2120 ÷ 33? (a) 710 (b) 71 (c) 7100
  23. 23.Best estimate of 4619 ÷ 59? (a) 77 (b) 7700 (c) 770
  24. 24.√74 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.6 (d) 8.5
  25. 25.√48 to 1 decimal place? (a) 7.1 (b) 6.9 (c) 6.8 (d) 7.0
  26. 26.√80 to 1 decimal place? (a) 8.9 (b) 8.7 (c) 9.0 (d) 8.8
  27. 27.√69 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.5 (d) 8.2
  28. 28.Best estimate of 1609 ÷ 33? (a) 540 (b) 5400 (c) 54
  29. 29.Best estimate of 4986 ÷ 79? (a) 620 (b) 6200 (c) 62
  30. 30.√65 to 1 decimal place? (a) 8.1 (b) 8.3 (c) 8.2 (d) 8.0
  31. 31.√63 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 8.2 (d) 7.9
  32. 32.Best estimate of 2220 ÷ 52? (a) 4400 (b) 440 (c) 44
  33. 33.Best estimate of 391 ÷ 28? (a) 1300 (b) 13 (c) 130
  34. 34.Best estimate of 5878 ÷ 82? (a) 730 (b) 7300 (c) 73
  35. 35.Best estimate of 1191 ÷ 46? (a) 24 (b) 240 (c) 2400
  36. 36.Best estimate of 1283 ÷ 43? (a) 3200 (b) 320 (c) 32
  37. 37.Best estimate of 1310 ÷ 54? (a) 260 (b) 26 (c) 2600
  38. 38.Best estimate of 1340 ÷ 51? (a) 27 (b) 270 (c) 2700
  39. 39.Best estimate of 2440 ÷ 46? (a) 4900 (b) 490 (c) 49
  40. 40.Best estimate of 1552 ÷ 81? (a) 19 (b) 1900 (c) 190

Answer key

  1. 94
  2. 59
  3. 4.5
  4. 80
  5. 27
  6. 6.8
  7. 18
  8. 7.3
  9. 29
  10. 31
  11. 70
  12. 5.1
  13. 6.5
  14. 50
  15. 92
  16. 6.3
  17. 8.1
  18. 4.6
  19. 97
  20. 6.1
  21. 8.8
  22. 71
  23. 77
  24. 8.6
  25. 6.9
  26. 8.9
  27. 8.3
  28. 54
  29. 62
  30. 8.1
  31. 7.9
  32. 44
  33. 13
  34. 73
  35. 24
  36. 32
  37. 26
  38. 27
  39. 49
  40. 19

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