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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 53 · 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 429 ÷ 23? (a) 21 (b) 210 (c) 2100
  2. 2.Best estimate of 7771 ÷ 86? (a) 8600 (b) 860 (c) 86
  3. 3.Best estimate of 3437 ÷ 47? (a) 69 (b) 6900 (c) 690
  4. 4.Best estimate of 2244 ÷ 42? (a) 5600 (b) 56 (c) 560
  5. 5.√55 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.3 (d) 7.6
  6. 6.Best estimate of 6215 ÷ 68? (a) 890 (b) 8900 (c) 89
  7. 7.√66 to 1 decimal place? (a) 8.2 (b) 8.0 (c) 7.9 (d) 8.1
  8. 8.√29 to 1 decimal place? (a) 5.4 (b) 5.5 (c) 5.3 (d) 5.2
  9. 9.Best estimate of 5877 ÷ 82? (a) 730 (b) 7300 (c) 73
  10. 10.Best estimate of 3448 ÷ 69? (a) 49 (b) 490 (c) 4900
  11. 11.√80 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 9.0 (d) 8.7
  12. 12.√34 to 1 decimal place? (a) 5.7 (b) 6.0 (c) 5.8 (d) 5.9
  13. 13.Best estimate of 761 ÷ 39? (a) 190 (b) 19 (c) 1900
  14. 14.√94 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 10.0 (d) 9.9
  15. 15.Best estimate of 2211 ÷ 52? (a) 440 (b) 4400 (c) 44
  16. 16.Best estimate of 3995 ÷ 87? (a) 4400 (b) 440 (c) 44
  17. 17.√27 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.5 (d) 5.2
  18. 18.√59 to 1 decimal place? (a) 7.6 (b) 7.7 (c) 7.5 (d) 7.4
  19. 19.Best estimate of 4187 ÷ 82? (a) 52 (b) 5200 (c) 520
  20. 20.√67 to 1 decimal place? (a) 8.0 (b) 8.3 (c) 8.2 (d) 8.1
  21. 21.√50 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 7.1 (d) 7.2
  22. 22.Best estimate of 1792 ÷ 62? (a) 300 (b) 30 (c) 3000
  23. 23.√61 to 1 decimal place? (a) 8.0 (b) 7.7 (c) 7.9 (d) 7.8
  24. 24.Best estimate of 1541 ÷ 62? (a) 260 (b) 2600 (c) 26
  25. 25.√30 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.6 (d) 5.5
  26. 26.Best estimate of 896 ÷ 56? (a) 150 (b) 15 (c) 1500
  27. 27.Best estimate of 1320 ÷ 56? (a) 22 (b) 220 (c) 2200
  28. 28.Best estimate of 2094 ÷ 39? (a) 52 (b) 5200 (c) 520
  29. 29.Best estimate of 2509 ÷ 39? (a) 6300 (b) 630 (c) 63
  30. 30.√31 to 1 decimal place? (a) 5.8 (b) 5.5 (c) 5.6 (d) 5.7
  31. 31.Best estimate of 3581 ÷ 43? (a) 900 (b) 90 (c) 9000
  32. 32.Best estimate of 2022 ÷ 33? (a) 670 (b) 67 (c) 6700
  33. 33.Best estimate of 3977 ÷ 77? (a) 50 (b) 500 (c) 5000
  34. 34.√69 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.4 (d) 8.3
  35. 35.√78 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.7 (d) 8.9
  36. 36.√41 to 1 decimal place? (a) 6.2 (b) 6.5 (c) 6.4 (d) 6.3
  37. 37.√40 to 1 decimal place? (a) 6.1 (b) 6.0 (c) 6.2 (d) 6.3
  38. 38.Best estimate of 3311 ÷ 61? (a) 55 (b) 550 (c) 5500
  39. 39.Best estimate of 6681 ÷ 79? (a) 84 (b) 8400 (c) 840
  40. 40.√26 to 1 decimal place? (a) 5.2 (b) 5.1 (c) 5.0 (d) 5.3

Answer key

  1. 21
  2. 86
  3. 69
  4. 56
  5. 7.4
  6. 89
  7. 8.1
  8. 5.4
  9. 73
  10. 49
  11. 8.9
  12. 5.8
  13. 19
  14. 9.7
  15. 44
  16. 44
  17. 5.2
  18. 7.7
  19. 52
  20. 8.2
  21. 7.1
  22. 30
  23. 7.8
  24. 26
  25. 5.5
  26. 15
  27. 22
  28. 52
  29. 63
  30. 5.6
  31. 90
  32. 67
  33. 50
  34. 8.3
  35. 8.8
  36. 6.4
  37. 6.3
  38. 55
  39. 84
  40. 5.1

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