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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 236 · 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.√87 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 9.3 (d) 9.2
  2. 2.Best estimate of 7831 ÷ 89? (a) 8700 (b) 870 (c) 87
  3. 3.√47 to 1 decimal place? (a) 7.1 (b) 6.9 (c) 7.0 (d) 7.2
  4. 4.Best estimate of 1525 ÷ 66? (a) 22 (b) 2200 (c) 220
  5. 5.√75 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.8 (d) 8.5
  6. 6.√29 to 1 decimal place? (a) 5.4 (b) 5.2 (c) 5.3 (d) 5.5
  7. 7.Best estimate of 1149 ÷ 38? (a) 290 (b) 2900 (c) 29
  8. 8.Best estimate of 5285 ÷ 86? (a) 5900 (b) 590 (c) 59
  9. 9.√21 to 1 decimal place? (a) 4.7 (b) 4.8 (c) 4.9 (d) 4.6
  10. 10.Best estimate of 2785 ÷ 32? (a) 9300 (b) 93 (c) 930
  11. 11.√24 to 1 decimal place? (a) 5.0 (b) 4.9 (c) 4.8 (d) 4.7
  12. 12.Best estimate of 1636 ÷ 73? (a) 2300 (b) 23 (c) 230
  13. 13.Best estimate of 4420 ÷ 52? (a) 88 (b) 880 (c) 8800
  14. 14.Best estimate of 1347 ÷ 42? (a) 340 (b) 3400 (c) 34
  15. 15.√43 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.8 (d) 6.9
  16. 16.Best estimate of 1717 ÷ 72? (a) 250 (b) 25 (c) 2500
  17. 17.√35 to 1 decimal place? (a) 6.1 (b) 5.9 (c) 6.2 (d) 6.0
  18. 18.√50 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 7.3 (d) 7.0
  19. 19.Best estimate of 497 ÷ 29? (a) 17 (b) 170 (c) 1700
  20. 20.Best estimate of 356 ÷ 28? (a) 1200 (b) 120 (c) 12
  21. 21.√88 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 9.3 (d) 9.4
  22. 22.√74 to 1 decimal place? (a) 8.6 (b) 8.4 (c) 8.5 (d) 8.3
  23. 23.Best estimate of 2628 ÷ 42? (a) 660 (b) 6600 (c) 66
  24. 24.Best estimate of 6790 ÷ 73? (a) 9700 (b) 97 (c) 970
  25. 25.Best estimate of 3039 ÷ 62? (a) 5100 (b) 51 (c) 510
  26. 26.Best estimate of 2020 ÷ 48? (a) 4000 (b) 40 (c) 400
  27. 27.√62 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 8.2 (d) 7.9
  28. 28.Best estimate of 4004 ÷ 58? (a) 67 (b) 670 (c) 6700
  29. 29.√84 to 1 decimal place? (a) 9.2 (b) 9.5 (c) 9.4 (d) 9.3
  30. 30.Best estimate of 2051 ÷ 36? (a) 5100 (b) 51 (c) 510
  31. 31.Best estimate of 1791 ÷ 56? (a) 30 (b) 300 (c) 3000
  32. 32.√31 to 1 decimal place? (a) 5.6 (b) 5.3 (c) 5.5 (d) 5.4
  33. 33.√92 to 1 decimal place? (a) 9.7 (b) 9.9 (c) 9.6 (d) 9.8
  34. 34.√34 to 1 decimal place? (a) 6.0 (b) 5.9 (c) 5.8 (d) 6.1
  35. 35.Best estimate of 3773 ÷ 79? (a) 470 (b) 47 (c) 4700
  36. 36.√55 to 1 decimal place? (a) 7.4 (b) 7.6 (c) 7.5 (d) 7.3
  37. 37.Best estimate of 2745 ÷ 74? (a) 390 (b) 39 (c) 3900
  38. 38.Best estimate of 1584 ÷ 81? (a) 2000 (b) 200 (c) 20
  39. 39.√51 to 1 decimal place? (a) 7.1 (b) 6.9 (c) 7.0 (d) 7.2
  40. 40.√58 to 1 decimal place? (a) 7.6 (b) 7.7 (c) 7.5 (d) 7.4

Answer key

  1. 9.3
  2. 87
  3. 6.9
  4. 22
  5. 8.7
  6. 5.4
  7. 29
  8. 59
  9. 4.6
  10. 93
  11. 4.9
  12. 23
  13. 88
  14. 34
  15. 6.6
  16. 25
  17. 5.9
  18. 7.1
  19. 17
  20. 12
  21. 9.4
  22. 8.6
  23. 66
  24. 97
  25. 51
  26. 40
  27. 7.9
  28. 67
  29. 9.2
  30. 51
  31. 30
  32. 5.6
  33. 9.6
  34. 5.8
  35. 47
  36. 7.4
  37. 39
  38. 20
  39. 7.1
  40. 7.6

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