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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 588 · 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 6477 ÷ 86? (a) 720 (b) 72 (c) 7200
  2. 2.√50 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 6.8 (d) 6.9
  3. 3.√42 to 1 decimal place? (a) 6.6 (b) 6.4 (c) 6.3 (d) 6.5
  4. 4.√53 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.2 (d) 7.5
  5. 5.Best estimate of 3442 ÷ 69? (a) 4900 (b) 490 (c) 49
  6. 6.Best estimate of 5614 ÷ 77? (a) 70 (b) 700 (c) 7000
  7. 7.√37 to 1 decimal place? (a) 6.1 (b) 6.3 (c) 6.4 (d) 6.2
  8. 8.Best estimate of 2040 ÷ 64? (a) 34 (b) 3400 (c) 340
  9. 9.√94 to 1 decimal place? (a) 9.4 (b) 9.6 (c) 9.5 (d) 9.7
  10. 10.√44 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.6 (d) 6.9
  11. 11.√20 to 1 decimal place? (a) 4.7 (b) 4.4 (c) 4.6 (d) 4.5
  12. 12.Best estimate of 1114 ÷ 39? (a) 28 (b) 280 (c) 2800
  13. 13.√85 to 1 decimal place? (a) 9.0 (b) 9.2 (c) 9.1 (d) 8.9
  14. 14.√27 to 1 decimal place? (a) 5.3 (b) 5.5 (c) 5.2 (d) 5.4
  15. 15.Best estimate of 2032 ÷ 77? (a) 250 (b) 2500 (c) 25
  16. 16.Best estimate of 2049 ÷ 72? (a) 290 (b) 29 (c) 2900
  17. 17.Best estimate of 2715 ÷ 42? (a) 68 (b) 680 (c) 6800
  18. 18.√34 to 1 decimal place? (a) 5.9 (b) 5.8 (c) 5.6 (d) 5.7
  19. 19.Best estimate of 686 ÷ 48? (a) 140 (b) 1400 (c) 14
  20. 20.Best estimate of 4682 ÷ 76? (a) 59 (b) 5900 (c) 590
  21. 21.√40 to 1 decimal place? (a) 6.1 (b) 6.0 (c) 6.3 (d) 6.2
  22. 22.Best estimate of 705 ÷ 26? (a) 240 (b) 24 (c) 2400
  23. 23.Best estimate of 1729 ÷ 39? (a) 4300 (b) 430 (c) 43
  24. 24.√77 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 8.7 (d) 9.0
  25. 25.√56 to 1 decimal place? (a) 7.8 (b) 7.6 (c) 7.7 (d) 7.5
  26. 26.Best estimate of 999 ÷ 36? (a) 2500 (b) 25 (c) 250
  27. 27.Best estimate of 6035 ÷ 63? (a) 101 (b) 10100 (c) 1010
  28. 28.Best estimate of 1829 ÷ 23? (a) 910 (b) 91 (c) 9100
  29. 29.Best estimate of 4437 ÷ 56? (a) 740 (b) 74 (c) 7400
  30. 30.√46 to 1 decimal place? (a) 6.9 (b) 6.8 (c) 6.7 (d) 6.6
  31. 31.√58 to 1 decimal place? (a) 7.4 (b) 7.7 (c) 7.6 (d) 7.5
  32. 32.Best estimate of 4058 ÷ 44? (a) 10100 (b) 101 (c) 1010
  33. 33.Best estimate of 2522 ÷ 27? (a) 840 (b) 84 (c) 8400
  34. 34.√82 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 9.0 (d) 8.9
  35. 35.√47 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 7.2 (d) 6.9
  36. 36.Best estimate of 4774 ÷ 63? (a) 8000 (b) 800 (c) 80
  37. 37.√84 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.2 (d) 9.5
  38. 38.Best estimate of 2528 ÷ 51? (a) 510 (b) 51 (c) 5100
  39. 39.Best estimate of 1377 ÷ 46? (a) 2800 (b) 280 (c) 28
  40. 40.Best estimate of 2665 ÷ 32? (a) 890 (b) 89 (c) 8900

Answer key

  1. 72
  2. 7.1
  3. 6.5
  4. 7.3
  5. 49
  6. 70
  7. 6.1
  8. 34
  9. 9.7
  10. 6.6
  11. 4.5
  12. 28
  13. 9.2
  14. 5.2
  15. 25
  16. 29
  17. 68
  18. 5.8
  19. 14
  20. 59
  21. 6.3
  22. 24
  23. 43
  24. 8.8
  25. 7.5
  26. 25
  27. 101
  28. 91
  29. 74
  30. 6.8
  31. 7.6
  32. 101
  33. 84
  34. 9.1
  35. 6.9
  36. 80
  37. 9.2
  38. 51
  39. 28
  40. 89

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