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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 395 · 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.√74 to 1 decimal place? (a) 8.5 (b) 8.7 (c) 8.4 (d) 8.6
  2. 2.Best estimate of 1037 ÷ 29? (a) 350 (b) 3500 (c) 35
  3. 3.Best estimate of 2929 ÷ 72? (a) 4200 (b) 42 (c) 420
  4. 4.√82 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 8.9 (d) 8.8
  5. 5.Best estimate of 1418 ÷ 37? (a) 35 (b) 3500 (c) 350
  6. 6.Best estimate of 1919 ÷ 86? (a) 21 (b) 210 (c) 2100
  7. 7.Best estimate of 3854 ÷ 81? (a) 480 (b) 48 (c) 4800
  8. 8.Best estimate of 2026 ÷ 61? (a) 340 (b) 34 (c) 3400
  9. 9.√37 to 1 decimal place? (a) 6.0 (b) 6.2 (c) 6.3 (d) 6.1
  10. 10.√38 to 1 decimal place? (a) 6.2 (b) 6.0 (c) 5.9 (d) 6.1
  11. 11.Best estimate of 3431 ÷ 74? (a) 49 (b) 490 (c) 4900
  12. 12.Best estimate of 1293 ÷ 32? (a) 430 (b) 4300 (c) 43
  13. 13.√56 to 1 decimal place? (a) 7.5 (b) 7.7 (c) 7.4 (d) 7.6
  14. 14.√78 to 1 decimal place? (a) 9.1 (b) 8.8 (c) 8.9 (d) 9.0
  15. 15.Best estimate of 2733 ÷ 54? (a) 55 (b) 550 (c) 5500
  16. 16.√90 to 1 decimal place? (a) 9.6 (b) 9.3 (c) 9.4 (d) 9.5
  17. 17.Best estimate of 1753 ÷ 24? (a) 880 (b) 8800 (c) 88
  18. 18.Best estimate of 3040 ÷ 33? (a) 1010 (b) 10100 (c) 101
  19. 19.√47 to 1 decimal place? (a) 7.1 (b) 6.9 (c) 6.8 (d) 7.0
  20. 20.√94 to 1 decimal place? (a) 9.9 (b) 9.8 (c) 9.7 (d) 9.6
  21. 21.Best estimate of 4102 ÷ 53? (a) 82 (b) 820 (c) 8200
  22. 22.Best estimate of 6322 ÷ 66? (a) 9000 (b) 90 (c) 900
  23. 23.Best estimate of 1777 ÷ 71? (a) 250 (b) 25 (c) 2500
  24. 24.Best estimate of 816 ÷ 66? (a) 120 (b) 12 (c) 1200
  25. 25.Best estimate of 4877 ÷ 86? (a) 540 (b) 54 (c) 5400
  26. 26.Best estimate of 1329 ÷ 37? (a) 33 (b) 330 (c) 3300
  27. 27.√62 to 1 decimal place? (a) 8.2 (b) 8.0 (c) 7.9 (d) 8.1
  28. 28.Best estimate of 2636 ÷ 31? (a) 88 (b) 880 (c) 8800
  29. 29.Best estimate of 4247 ÷ 86? (a) 4700 (b) 470 (c) 47
  30. 30.√69 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 8.3 (d) 8.2
  31. 31.√61 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 7.8 (d) 7.9
  32. 32.Best estimate of 1053 ÷ 33? (a) 3500 (b) 35 (c) 350
  33. 33.Best estimate of 1784 ÷ 58? (a) 3000 (b) 300 (c) 30
  34. 34.Best estimate of 1538 ÷ 32? (a) 510 (b) 5100 (c) 51
  35. 35.√35 to 1 decimal place? (a) 6.0 (b) 6.1 (c) 5.8 (d) 5.9
  36. 36.Best estimate of 5068 ÷ 64? (a) 84 (b) 8400 (c) 840
  37. 37.Best estimate of 3071 ÷ 79? (a) 38 (b) 380 (c) 3800
  38. 38.Best estimate of 3405 ÷ 42? (a) 85 (b) 850 (c) 8500
  39. 39.Best estimate of 1182 ÷ 36? (a) 3000 (b) 30 (c) 300
  40. 40.Best estimate of 4391 ÷ 51? (a) 8800 (b) 88 (c) 880

Answer key

  1. 8.6
  2. 35
  3. 42
  4. 9.1
  5. 35
  6. 21
  7. 48
  8. 34
  9. 6.1
  10. 6.2
  11. 49
  12. 43
  13. 7.5
  14. 8.8
  15. 55
  16. 9.5
  17. 88
  18. 101
  19. 6.9
  20. 9.7
  21. 82
  22. 90
  23. 25
  24. 12
  25. 54
  26. 33
  27. 7.9
  28. 88
  29. 47
  30. 8.3
  31. 7.8
  32. 35
  33. 30
  34. 51
  35. 5.9
  36. 84
  37. 38
  38. 85
  39. 30
  40. 88

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