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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 318 · 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 1653 ÷ 67? (a) 2400 (b) 24 (c) 240
  2. 2.Best estimate of 4086 ÷ 89? (a) 45 (b) 4500 (c) 450
  3. 3.Best estimate of 5219 ÷ 58? (a) 8700 (b) 870 (c) 87
  4. 4.√22 to 1 decimal place? (a) 4.9 (b) 4.7 (c) 4.6 (d) 4.8
  5. 5.√96 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 9.8 (d) 9.6
  6. 6.Best estimate of 1006 ÷ 32? (a) 3400 (b) 340 (c) 34
  7. 7.√44 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.9 (d) 6.6
  8. 8.Best estimate of 2023 ÷ 86? (a) 2200 (b) 22 (c) 220
  9. 9.Best estimate of 620 ÷ 24? (a) 310 (b) 3100 (c) 31
  10. 10.Best estimate of 4164 ÷ 88? (a) 46 (b) 460 (c) 4600
  11. 11.√83 to 1 decimal place? (a) 9.1 (b) 8.8 (c) 8.9 (d) 9.0
  12. 12.Best estimate of 2561 ÷ 66? (a) 3700 (b) 37 (c) 370
  13. 13.Best estimate of 4128 ÷ 86? (a) 46 (b) 4600 (c) 460
  14. 14.Best estimate of 1745 ÷ 58? (a) 290 (b) 29 (c) 2900
  15. 15.Best estimate of 842 ÷ 56? (a) 14 (b) 1400 (c) 140
  16. 16.Best estimate of 3051 ÷ 76? (a) 380 (b) 38 (c) 3800
  17. 17.Best estimate of 2145 ÷ 86? (a) 2400 (b) 240 (c) 24
  18. 18.Best estimate of 5599 ÷ 61? (a) 9300 (b) 93 (c) 930
  19. 19.Best estimate of 1761 ÷ 52? (a) 350 (b) 3500 (c) 35
  20. 20.√32 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.5 (d) 5.6
  21. 21.√98 to 1 decimal place? (a) 10.0 (b) 10.1 (c) 10.2 (d) 9.9
  22. 22.√34 to 1 decimal place? (a) 5.9 (b) 6.1 (c) 5.8 (d) 6.0
  23. 23.Best estimate of 1738 ÷ 46? (a) 35 (b) 350 (c) 3500
  24. 24.Best estimate of 786 ÷ 28? (a) 260 (b) 2600 (c) 26
  25. 25.Best estimate of 4397 ÷ 48? (a) 8800 (b) 880 (c) 88
  26. 26.√61 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 7.6 (d) 7.7
  27. 27.√31 to 1 decimal place? (a) 5.6 (b) 5.8 (c) 5.9 (d) 5.7
  28. 28.√76 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 8.6 (d) 8.7
  29. 29.Best estimate of 1502 ÷ 62? (a) 2500 (b) 250 (c) 25
  30. 30.Best estimate of 2110 ÷ 53? (a) 420 (b) 4200 (c) 42
  31. 31.√51 to 1 decimal place? (a) 7.0 (b) 7.1 (c) 7.2 (d) 6.9
  32. 32.√66 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 8.1 (d) 7.8
  33. 33.√35 to 1 decimal place? (a) 5.9 (b) 6.1 (c) 6.0 (d) 6.2
  34. 34.Best estimate of 3332 ÷ 64? (a) 560 (b) 56 (c) 5600
  35. 35.Best estimate of 3556 ÷ 39? (a) 890 (b) 8900 (c) 89
  36. 36.√74 to 1 decimal place? (a) 8.5 (b) 8.7 (c) 8.6 (d) 8.4
  37. 37.Best estimate of 2962 ÷ 81? (a) 370 (b) 3700 (c) 37
  38. 38.√37 to 1 decimal place? (a) 6.2 (b) 5.9 (c) 6.0 (d) 6.1
  39. 39.√27 to 1 decimal place? (a) 5.4 (b) 5.5 (c) 5.3 (d) 5.2
  40. 40.Best estimate of 6251 ÷ 67? (a) 890 (b) 8900 (c) 89

Answer key

  1. 24
  2. 45
  3. 87
  4. 4.7
  5. 9.8
  6. 34
  7. 6.6
  8. 22
  9. 31
  10. 46
  11. 9.1
  12. 37
  13. 46
  14. 29
  15. 14
  16. 38
  17. 24
  18. 93
  19. 35
  20. 5.7
  21. 9.9
  22. 5.8
  23. 35
  24. 26
  25. 88
  26. 7.8
  27. 5.6
  28. 8.7
  29. 25
  30. 42
  31. 7.1
  32. 8.1
  33. 5.9
  34. 56
  35. 89
  36. 8.6
  37. 37
  38. 6.1
  39. 5.2
  40. 89

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