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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 792 · 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 824 ÷ 21? (a) 410 (b) 41 (c) 4100
  2. 2.Best estimate of 1721 ÷ 56? (a) 29 (b) 2900 (c) 290
  3. 3.Best estimate of 2704 ÷ 74? (a) 39 (b) 3900 (c) 390
  4. 4.√98 to 1 decimal place? (a) 10.0 (b) 9.7 (c) 9.9 (d) 9.8
  5. 5.√41 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.3 (d) 6.4
  6. 6.Best estimate of 3220 ÷ 39? (a) 810 (b) 81 (c) 8100
  7. 7.Best estimate of 1085 ÷ 83? (a) 14 (b) 140 (c) 1400
  8. 8.√51 to 1 decimal place? (a) 7.0 (b) 6.9 (c) 7.1 (d) 6.8
  9. 9.√50 to 1 decimal place? (a) 7.3 (b) 7.1 (c) 7.2 (d) 7.4
  10. 10.Best estimate of 1633 ÷ 29? (a) 54 (b) 540 (c) 5400
  11. 11.Best estimate of 3648 ÷ 44? (a) 910 (b) 91 (c) 9100
  12. 12.Best estimate of 4384 ÷ 72? (a) 630 (b) 63 (c) 6300
  13. 13.√55 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.6 (d) 7.7
  14. 14.√42 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.6 (d) 6.5
  15. 15.√31 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.4 (d) 5.5
  16. 16.√61 to 1 decimal place? (a) 8.0 (b) 7.7 (c) 7.8 (d) 7.9
  17. 17.Best estimate of 3211 ÷ 64? (a) 5400 (b) 54 (c) 540
  18. 18.Best estimate of 2865 ÷ 38? (a) 720 (b) 72 (c) 7200
  19. 19.Best estimate of 6870 ÷ 74? (a) 980 (b) 98 (c) 9800
  20. 20.Best estimate of 2278 ÷ 76? (a) 2800 (b) 280 (c) 28
  21. 21.√90 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.8 (d) 9.5
  22. 22.√26 to 1 decimal place? (a) 5.0 (b) 4.8 (c) 4.9 (d) 5.1
  23. 23.Best estimate of 4294 ÷ 76? (a) 54 (b) 5400 (c) 540
  24. 24.Best estimate of 6962 ÷ 89? (a) 7700 (b) 770 (c) 77
  25. 25.Best estimate of 2142 ÷ 36? (a) 5400 (b) 540 (c) 54
  26. 26.Best estimate of 1246 ÷ 66? (a) 1800 (b) 18 (c) 180
  27. 27.Best estimate of 1124 ÷ 34? (a) 3700 (b) 37 (c) 370
  28. 28.Best estimate of 1208 ÷ 57? (a) 20 (b) 200 (c) 2000
  29. 29.Best estimate of 2313 ÷ 26? (a) 77 (b) 7700 (c) 770
  30. 30.Best estimate of 1921 ÷ 52? (a) 380 (b) 38 (c) 3800
  31. 31.√28 to 1 decimal place? (a) 5.2 (b) 5.4 (c) 5.3 (d) 5.5
  32. 32.Best estimate of 1272 ÷ 36? (a) 32 (b) 3200 (c) 320
  33. 33.√62 to 1 decimal place? (a) 8.1 (b) 7.9 (c) 8.2 (d) 8.0
  34. 34.√21 to 1 decimal place? (a) 4.4 (b) 4.3 (c) 4.5 (d) 4.6
  35. 35.√63 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.0 (d) 7.9
  36. 36.Best estimate of 707 ÷ 23? (a) 350 (b) 35 (c) 3500
  37. 37.√77 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 8.7 (d) 8.8
  38. 38.Best estimate of 386 ÷ 32? (a) 13 (b) 130 (c) 1300
  39. 39.Best estimate of 6725 ÷ 72? (a) 96 (b) 960 (c) 9600
  40. 40.√71 to 1 decimal place? (a) 8.4 (b) 8.1 (c) 8.2 (d) 8.3

Answer key

  1. 41
  2. 29
  3. 39
  4. 9.9
  5. 6.4
  6. 81
  7. 14
  8. 7.1
  9. 7.1
  10. 54
  11. 91
  12. 63
  13. 7.4
  14. 6.5
  15. 5.6
  16. 7.8
  17. 54
  18. 72
  19. 98
  20. 28
  21. 9.5
  22. 5.1
  23. 54
  24. 77
  25. 54
  26. 18
  27. 37
  28. 20
  29. 77
  30. 38
  31. 5.3
  32. 32
  33. 7.9
  34. 4.6
  35. 7.9
  36. 35
  37. 8.8
  38. 13
  39. 96
  40. 8.4

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