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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 32 · 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.√69 to 1 decimal place? (a) 8.3 (b) 8.5 (c) 8.4 (d) 8.2
  2. 2.√82 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.2 (d) 9.1
  3. 3.Best estimate of 1979 ÷ 36? (a) 4900 (b) 49 (c) 490
  4. 4.Best estimate of 2797 ÷ 46? (a) 560 (b) 56 (c) 5600
  5. 5.√96 to 1 decimal place? (a) 9.9 (b) 9.8 (c) 9.7 (d) 9.6
  6. 6.Best estimate of 1123 ÷ 24? (a) 5600 (b) 560 (c) 56
  7. 7.Best estimate of 6853 ÷ 72? (a) 980 (b) 98 (c) 9800
  8. 8.Best estimate of 3009 ÷ 64? (a) 5000 (b) 500 (c) 50
  9. 9.Best estimate of 2146 ÷ 26? (a) 7200 (b) 720 (c) 72
  10. 10.√24 to 1 decimal place? (a) 4.9 (b) 4.7 (c) 4.8 (d) 5.0
  11. 11.√88 to 1 decimal place? (a) 9.4 (b) 9.7 (c) 9.6 (d) 9.5
  12. 12.Best estimate of 1777 ÷ 33? (a) 59 (b) 5900 (c) 590
  13. 13.Best estimate of 2586 ÷ 32? (a) 86 (b) 860 (c) 8600
  14. 14.Best estimate of 2266 ÷ 37? (a) 57 (b) 570 (c) 5700
  15. 15.√50 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 6.8 (d) 6.9
  16. 16.√53 to 1 decimal place? (a) 7.5 (b) 7.3 (c) 7.6 (d) 7.4
  17. 17.√30 to 1 decimal place? (a) 5.4 (b) 5.6 (c) 5.5 (d) 5.3
  18. 18.√63 to 1 decimal place? (a) 7.9 (b) 7.7 (c) 7.8 (d) 7.6
  19. 19.Best estimate of 5933 ÷ 67? (a) 8500 (b) 85 (c) 850
  20. 20.Best estimate of 1320 ÷ 39? (a) 33 (b) 3300 (c) 330
  21. 21.Best estimate of 6517 ÷ 72? (a) 93 (b) 9300 (c) 930
  22. 22.Best estimate of 609 ÷ 32? (a) 200 (b) 2000 (c) 20
  23. 23.Best estimate of 5341 ÷ 62? (a) 89 (b) 8900 (c) 890
  24. 24.Best estimate of 2143 ÷ 31? (a) 710 (b) 7100 (c) 71
  25. 25.√21 to 1 decimal place? (a) 4.9 (b) 4.7 (c) 4.6 (d) 4.8
  26. 26.Best estimate of 2242 ÷ 66? (a) 3200 (b) 320 (c) 32
  27. 27.Best estimate of 2767 ÷ 31? (a) 9200 (b) 92 (c) 920
  28. 28.Best estimate of 2706 ÷ 29? (a) 900 (b) 90 (c) 9000
  29. 29.Best estimate of 3871 ÷ 53? (a) 7700 (b) 770 (c) 77
  30. 30.Best estimate of 934 ÷ 44? (a) 23 (b) 2300 (c) 230
  31. 31.Best estimate of 6245 ÷ 76? (a) 780 (b) 78 (c) 7800
  32. 32.Best estimate of 2582 ÷ 36? (a) 650 (b) 6500 (c) 65
  33. 33.Best estimate of 6195 ÷ 76? (a) 77 (b) 770 (c) 7700
  34. 34.√61 to 1 decimal place? (a) 7.7 (b) 8.0 (c) 7.8 (d) 7.9
  35. 35.√51 to 1 decimal place? (a) 7.2 (b) 7.3 (c) 7.1 (d) 7.4
  36. 36.Best estimate of 1237 ÷ 22? (a) 62 (b) 620 (c) 6200
  37. 37.Best estimate of 785 ÷ 48? (a) 16 (b) 1600 (c) 160
  38. 38.Best estimate of 6228 ÷ 86? (a) 6900 (b) 690 (c) 69
  39. 39.√34 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 6.0 (d) 5.7
  40. 40.√94 to 1 decimal place? (a) 9.4 (b) 9.7 (c) 9.5 (d) 9.6

Answer key

  1. 8.3
  2. 9.1
  3. 49
  4. 56
  5. 9.8
  6. 56
  7. 98
  8. 50
  9. 72
  10. 4.9
  11. 9.4
  12. 59
  13. 86
  14. 57
  15. 7.1
  16. 7.3
  17. 5.5
  18. 7.9
  19. 85
  20. 33
  21. 93
  22. 20
  23. 89
  24. 71
  25. 4.6
  26. 32
  27. 92
  28. 90
  29. 77
  30. 23
  31. 78
  32. 65
  33. 77
  34. 7.8
  35. 7.1
  36. 62
  37. 16
  38. 69
  39. 5.8
  40. 9.7

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