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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 95 · 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.√78 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 9.0 (d) 9.1
  2. 2.Best estimate of 2440 ÷ 66? (a) 35 (b) 350 (c) 3500
  3. 3.√71 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.2 (d) 8.1
  4. 4.√30 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.5 (d) 5.6
  5. 5.√58 to 1 decimal place? (a) 7.6 (b) 7.7 (c) 7.5 (d) 7.8
  6. 6.Best estimate of 1588 ÷ 59? (a) 260 (b) 2600 (c) 26
  7. 7.√92 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.6 (d) 9.3
  8. 8.Best estimate of 4598 ÷ 53? (a) 920 (b) 92 (c) 9200
  9. 9.√20 to 1 decimal place? (a) 4.3 (b) 4.5 (c) 4.4 (d) 4.2
  10. 10.Best estimate of 2306 ÷ 47? (a) 460 (b) 46 (c) 4600
  11. 11.Best estimate of 344 ÷ 28? (a) 1100 (b) 110 (c) 11
  12. 12.Best estimate of 1279 ÷ 74? (a) 1800 (b) 180 (c) 18
  13. 13.√55 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.3 (d) 7.6
  14. 14.√51 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 6.9 (d) 7.2
  15. 15.Best estimate of 803 ÷ 39? (a) 2000 (b) 20 (c) 200
  16. 16.√59 to 1 decimal place? (a) 7.9 (b) 7.7 (c) 7.8 (d) 8.0
  17. 17.√53 to 1 decimal place? (a) 7.3 (b) 7.6 (c) 7.4 (d) 7.5
  18. 18.√31 to 1 decimal place? (a) 5.7 (b) 5.4 (c) 5.6 (d) 5.5
  19. 19.Best estimate of 2148 ÷ 34? (a) 7200 (b) 72 (c) 720
  20. 20.Best estimate of 4066 ÷ 56? (a) 680 (b) 6800 (c) 68
  21. 21.√27 to 1 decimal place? (a) 5.0 (b) 5.3 (c) 5.2 (d) 5.1
  22. 22.Best estimate of 4965 ÷ 52? (a) 99 (b) 990 (c) 9900
  23. 23.√66 to 1 decimal place? (a) 8.3 (b) 8.1 (c) 8.0 (d) 8.2
  24. 24.Best estimate of 4572 ÷ 76? (a) 5700 (b) 570 (c) 57
  25. 25.√61 to 1 decimal place? (a) 7.8 (b) 7.6 (c) 7.9 (d) 7.7
  26. 26.Best estimate of 3560 ÷ 52? (a) 710 (b) 7100 (c) 71
  27. 27.√41 to 1 decimal place? (a) 6.4 (b) 6.3 (c) 6.2 (d) 6.1
  28. 28.Best estimate of 768 ÷ 21? (a) 380 (b) 3800 (c) 38
  29. 29.Best estimate of 405 ÷ 23? (a) 200 (b) 20 (c) 2000
  30. 30.√42 to 1 decimal place? (a) 6.5 (b) 6.8 (c) 6.6 (d) 6.7
  31. 31.√69 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 8.2 (d) 8.3
  32. 32.√89 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.4 (d) 9.5
  33. 33.Best estimate of 1662 ÷ 62? (a) 2800 (b) 28 (c) 280
  34. 34.√40 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.5 (d) 6.2
  35. 35.Best estimate of 5043 ÷ 57? (a) 840 (b) 84 (c) 8400
  36. 36.√87 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.1 (d) 9.2
  37. 37.Best estimate of 1751 ÷ 62? (a) 2900 (b) 29 (c) 290
  38. 38.Best estimate of 1568 ÷ 27? (a) 520 (b) 52 (c) 5200
  39. 39.Best estimate of 6850 ÷ 73? (a) 98 (b) 9800 (c) 980
  40. 40.√94 to 1 decimal place? (a) 9.9 (b) 9.6 (c) 9.8 (d) 9.7

Answer key

  1. 8.8
  2. 35
  3. 8.4
  4. 5.5
  5. 7.6
  6. 26
  7. 9.6
  8. 92
  9. 4.5
  10. 46
  11. 11
  12. 18
  13. 7.4
  14. 7.1
  15. 20
  16. 7.7
  17. 7.3
  18. 5.6
  19. 72
  20. 68
  21. 5.2
  22. 99
  23. 8.1
  24. 57
  25. 7.8
  26. 71
  27. 6.4
  28. 38
  29. 20
  30. 6.5
  31. 8.3
  32. 9.4
  33. 28
  34. 6.3
  35. 84
  36. 9.3
  37. 29
  38. 52
  39. 98
  40. 9.7

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