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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 763 · 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.√20 to 1 decimal place? (a) 4.6 (b) 4.7 (c) 4.5 (d) 4.4
  2. 2.√59 to 1 decimal place? (a) 7.8 (b) 7.5 (c) 7.6 (d) 7.7
  3. 3.√74 to 1 decimal place? (a) 8.8 (b) 8.7 (c) 8.5 (d) 8.6
  4. 4.√88 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.4 (d) 9.1
  5. 5.√53 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.3 (d) 7.4
  6. 6.√76 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.7 (d) 8.4
  7. 7.Best estimate of 2945 ÷ 76? (a) 37 (b) 370 (c) 3700
  8. 8.√78 to 1 decimal place? (a) 9.1 (b) 8.9 (c) 8.8 (d) 9.0
  9. 9.Best estimate of 7522 ÷ 84? (a) 94 (b) 940 (c) 9400
  10. 10.√40 to 1 decimal place? (a) 6.2 (b) 6.5 (c) 6.4 (d) 6.3
  11. 11.√55 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 7.4 (d) 7.3
  12. 12.√44 to 1 decimal place? (a) 6.7 (b) 6.9 (c) 6.6 (d) 6.8
  13. 13.√50 to 1 decimal place? (a) 7.1 (b) 7.4 (c) 7.2 (d) 7.3
  14. 14.Best estimate of 3756 ÷ 52? (a) 750 (b) 7500 (c) 75
  15. 15.Best estimate of 3763 ÷ 68? (a) 54 (b) 5400 (c) 540
  16. 16.√66 to 1 decimal place? (a) 8.0 (b) 8.3 (c) 8.1 (d) 8.2
  17. 17.√27 to 1 decimal place? (a) 5.5 (b) 5.2 (c) 5.4 (d) 5.3
  18. 18.Best estimate of 306 ÷ 21? (a) 15 (b) 1500 (c) 150
  19. 19.√45 to 1 decimal place? (a) 6.7 (b) 6.9 (c) 7.0 (d) 6.8
  20. 20.√83 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 9.3 (d) 9.2
  21. 21.Best estimate of 3711 ÷ 46? (a) 74 (b) 7400 (c) 740
  22. 22.Best estimate of 2803 ÷ 33? (a) 930 (b) 9300 (c) 93
  23. 23.Best estimate of 3943 ÷ 42? (a) 990 (b) 9900 (c) 99
  24. 24.√82 to 1 decimal place? (a) 9.1 (b) 9.3 (c) 9.2 (d) 9.0
  25. 25.Best estimate of 3212 ÷ 57? (a) 540 (b) 5400 (c) 54
  26. 26.Best estimate of 2726 ÷ 56? (a) 45 (b) 450 (c) 4500
  27. 27.Best estimate of 390 ÷ 26? (a) 13 (b) 1300 (c) 130
  28. 28.Best estimate of 3091 ÷ 86? (a) 3400 (b) 34 (c) 340
  29. 29.√58 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.3 (d) 7.4
  30. 30.Best estimate of 2350 ÷ 36? (a) 59 (b) 590 (c) 5900
  31. 31.Best estimate of 3094 ÷ 89? (a) 3400 (b) 340 (c) 34
  32. 32.Best estimate of 1119 ÷ 72? (a) 160 (b) 1600 (c) 16
  33. 33.√89 to 1 decimal place? (a) 9.5 (b) 9.3 (c) 9.4 (d) 9.6
  34. 34.√29 to 1 decimal place? (a) 5.3 (b) 5.5 (c) 5.6 (d) 5.4
  35. 35.Best estimate of 1643 ÷ 68? (a) 23 (b) 2300 (c) 230
  36. 36.Best estimate of 1607 ÷ 24? (a) 8000 (b) 800 (c) 80
  37. 37.Best estimate of 520 ÷ 43? (a) 130 (b) 13 (c) 1300
  38. 38.√96 to 1 decimal place? (a) 10.0 (b) 10.1 (c) 9.9 (d) 9.8
  39. 39.Best estimate of 847 ÷ 32? (a) 280 (b) 28 (c) 2800
  40. 40.√42 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.5 (d) 6.2

Answer key

  1. 4.5
  2. 7.7
  3. 8.6
  4. 9.4
  5. 7.3
  6. 8.7
  7. 37
  8. 8.8
  9. 94
  10. 6.3
  11. 7.4
  12. 6.6
  13. 7.1
  14. 75
  15. 54
  16. 8.1
  17. 5.2
  18. 15
  19. 6.7
  20. 9.1
  21. 74
  22. 93
  23. 99
  24. 9.1
  25. 54
  26. 45
  27. 13
  28. 34
  29. 7.6
  30. 59
  31. 34
  32. 16
  33. 9.4
  34. 5.4
  35. 23
  36. 80
  37. 13
  38. 9.8
  39. 28
  40. 6.5

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