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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 814 · 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 5118 ÷ 66? (a) 7300 (b) 730 (c) 73
  2. 2.Best estimate of 1610 ÷ 66? (a) 230 (b) 2300 (c) 23
  3. 3.√48 to 1 decimal place? (a) 7.1 (b) 6.8 (c) 6.9 (d) 7.0
  4. 4.√96 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 9.8 (d) 10.0
  5. 5.√56 to 1 decimal place? (a) 7.3 (b) 7.6 (c) 7.5 (d) 7.4
  6. 6.Best estimate of 3837 ÷ 56? (a) 6400 (b) 640 (c) 64
  7. 7.√21 to 1 decimal place? (a) 4.5 (b) 4.7 (c) 4.6 (d) 4.8
  8. 8.√61 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 7.9 (d) 7.8
  9. 9.Best estimate of 2843 ÷ 39? (a) 7100 (b) 710 (c) 71
  10. 10.√55 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.3 (d) 7.4
  11. 11.Best estimate of 4516 ÷ 79? (a) 5600 (b) 560 (c) 56
  12. 12.Best estimate of 4209 ÷ 49? (a) 84 (b) 8400 (c) 840
  13. 13.√34 to 1 decimal place? (a) 5.6 (b) 5.7 (c) 5.9 (d) 5.8
  14. 14.√23 to 1 decimal place? (a) 4.6 (b) 4.5 (c) 4.8 (d) 4.7
  15. 15.Best estimate of 279 ÷ 21? (a) 1400 (b) 14 (c) 140
  16. 16.Best estimate of 1973 ÷ 88? (a) 22 (b) 220 (c) 2200
  17. 17.√75 to 1 decimal place? (a) 8.5 (b) 8.8 (c) 8.6 (d) 8.7
  18. 18.Best estimate of 4673 ÷ 52? (a) 9300 (b) 930 (c) 93
  19. 19.Best estimate of 1728 ÷ 44? (a) 4300 (b) 43 (c) 430
  20. 20.Best estimate of 2334 ÷ 62? (a) 390 (b) 39 (c) 3900
  21. 21.√78 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.6 (d) 8.7
  22. 22.Best estimate of 3352 ÷ 86? (a) 3700 (b) 370 (c) 37
  23. 23.Best estimate of 1949 ÷ 52? (a) 39 (b) 3900 (c) 390
  24. 24.Best estimate of 1963 ÷ 21? (a) 980 (b) 98 (c) 9800
  25. 25.Best estimate of 2396 ÷ 26? (a) 8000 (b) 800 (c) 80
  26. 26.Best estimate of 1830 ÷ 59? (a) 310 (b) 3100 (c) 31
  27. 27.Best estimate of 3828 ÷ 72? (a) 55 (b) 550 (c) 5500
  28. 28.√37 to 1 decimal place? (a) 5.9 (b) 6.2 (c) 6.0 (d) 6.1
  29. 29.Best estimate of 522 ÷ 36? (a) 13 (b) 1300 (c) 130
  30. 30.√90 to 1 decimal place? (a) 9.5 (b) 9.3 (c) 9.4 (d) 9.6
  31. 31.Best estimate of 2202 ÷ 34? (a) 73 (b) 730 (c) 7300
  32. 32.√74 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.7 (d) 8.6
  33. 33.Best estimate of 1898 ÷ 61? (a) 32 (b) 320 (c) 3200
  34. 34.Best estimate of 5972 ÷ 79? (a) 7500 (b) 75 (c) 750
  35. 35.√46 to 1 decimal place? (a) 6.6 (b) 6.8 (c) 6.9 (d) 6.7
  36. 36.Best estimate of 1009 ÷ 47? (a) 20 (b) 2000 (c) 200
  37. 37.Best estimate of 1643 ÷ 43? (a) 410 (b) 4100 (c) 41
  38. 38.√94 to 1 decimal place? (a) 9.9 (b) 9.8 (c) 10.0 (d) 9.7
  39. 39.√65 to 1 decimal place? (a) 8.3 (b) 8.1 (c) 8.0 (d) 8.2
  40. 40.Best estimate of 547 ÷ 34? (a) 180 (b) 1800 (c) 18

Answer key

  1. 73
  2. 23
  3. 6.9
  4. 9.8
  5. 7.5
  6. 64
  7. 4.6
  8. 7.8
  9. 71
  10. 7.4
  11. 56
  12. 84
  13. 5.8
  14. 4.8
  15. 14
  16. 22
  17. 8.7
  18. 93
  19. 43
  20. 39
  21. 8.8
  22. 37
  23. 39
  24. 98
  25. 80
  26. 31
  27. 55
  28. 6.1
  29. 13
  30. 9.5
  31. 73
  32. 8.6
  33. 32
  34. 75
  35. 6.8
  36. 20
  37. 41
  38. 9.7
  39. 8.1
  40. 18

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