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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 819 · 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.√58 to 1 decimal place? (a) 7.7 (b) 7.9 (c) 7.6 (d) 7.8
  2. 2.Best estimate of 4808 ÷ 62? (a) 800 (b) 80 (c) 8000
  3. 3.Best estimate of 5185 ÷ 62? (a) 86 (b) 8600 (c) 860
  4. 4.√35 to 1 decimal place? (a) 5.9 (b) 6.0 (c) 6.1 (d) 5.8
  5. 5.Best estimate of 569 ÷ 31? (a) 1900 (b) 190 (c) 19
  6. 6.√34 to 1 decimal place? (a) 5.9 (b) 6.0 (c) 6.1 (d) 5.8
  7. 7.Best estimate of 3399 ÷ 76? (a) 42 (b) 420 (c) 4200
  8. 8.Best estimate of 3009 ÷ 77? (a) 380 (b) 3800 (c) 38
  9. 9.√67 to 1 decimal place? (a) 8.5 (b) 8.3 (c) 8.2 (d) 8.4
  10. 10.√42 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.3 (d) 6.4
  11. 11.Best estimate of 3386 ÷ 63? (a) 56 (b) 5600 (c) 560
  12. 12.Best estimate of 4698 ÷ 56? (a) 7800 (b) 780 (c) 78
  13. 13.√38 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.4 (d) 6.5
  14. 14.√32 to 1 decimal place? (a) 5.6 (b) 5.5 (c) 5.7 (d) 5.4
  15. 15.Best estimate of 3312 ÷ 58? (a) 55 (b) 5500 (c) 550
  16. 16.Best estimate of 4519 ÷ 79? (a) 5600 (b) 560 (c) 56
  17. 17.Best estimate of 1661 ÷ 84? (a) 2100 (b) 210 (c) 21
  18. 18.Best estimate of 4988 ÷ 68? (a) 71 (b) 7100 (c) 710
  19. 19.√26 to 1 decimal place? (a) 5.2 (b) 5.0 (c) 5.3 (d) 5.1
  20. 20.√69 to 1 decimal place? (a) 8.2 (b) 8.5 (c) 8.4 (d) 8.3
  21. 21.Best estimate of 3395 ÷ 76? (a) 420 (b) 4200 (c) 42
  22. 22.√50 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 6.9 (d) 7.2
  23. 23.Best estimate of 2179 ÷ 33? (a) 730 (b) 73 (c) 7300
  24. 24.√27 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.5 (d) 5.4
  25. 25.Best estimate of 969 ÷ 36? (a) 24 (b) 240 (c) 2400
  26. 26.√30 to 1 decimal place? (a) 5.4 (b) 5.6 (c) 5.5 (d) 5.3
  27. 27.√53 to 1 decimal place? (a) 7.3 (b) 7.4 (c) 7.5 (d) 7.6
  28. 28.Best estimate of 1255 ÷ 66? (a) 180 (b) 1800 (c) 18
  29. 29.Best estimate of 1574 ÷ 32? (a) 52 (b) 520 (c) 5200
  30. 30.Best estimate of 2756 ÷ 73? (a) 390 (b) 39 (c) 3900
  31. 31.Best estimate of 2330 ÷ 31? (a) 7800 (b) 780 (c) 78
  32. 32.Best estimate of 1188 ÷ 69? (a) 170 (b) 17 (c) 1700
  33. 33.√63 to 1 decimal place? (a) 8.0 (b) 7.9 (c) 8.2 (d) 8.1
  34. 34.√56 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.5 (d) 7.2
  35. 35.Best estimate of 3432 ÷ 42? (a) 860 (b) 8600 (c) 86
  36. 36.Best estimate of 2053 ÷ 67? (a) 290 (b) 2900 (c) 29
  37. 37.Best estimate of 6246 ÷ 69? (a) 8900 (b) 89 (c) 890
  38. 38.Best estimate of 4293 ÷ 63? (a) 720 (b) 7200 (c) 72
  39. 39.√52 to 1 decimal place? (a) 7.2 (b) 7.0 (c) 7.1 (d) 7.3
  40. 40.√98 to 1 decimal place? (a) 9.9 (b) 9.6 (c) 9.8 (d) 9.7

Answer key

  1. 7.6
  2. 80
  3. 86
  4. 5.9
  5. 19
  6. 5.8
  7. 42
  8. 38
  9. 8.2
  10. 6.5
  11. 56
  12. 78
  13. 6.2
  14. 5.7
  15. 55
  16. 56
  17. 21
  18. 71
  19. 5.1
  20. 8.3
  21. 42
  22. 7.1
  23. 73
  24. 5.2
  25. 24
  26. 5.5
  27. 7.3
  28. 18
  29. 52
  30. 39
  31. 78
  32. 17
  33. 7.9
  34. 7.5
  35. 86
  36. 29
  37. 89
  38. 72
  39. 7.2
  40. 9.9

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