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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 260 · 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.√27 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.0 (d) 5.1
  2. 2.Best estimate of 2973 ÷ 42? (a) 7400 (b) 740 (c) 74
  3. 3.√85 to 1 decimal place? (a) 9.0 (b) 9.2 (c) 8.9 (d) 9.1
  4. 4.Best estimate of 2736 ÷ 51? (a) 550 (b) 5500 (c) 55
  5. 5.√69 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.1 (d) 8.2
  6. 6.Best estimate of 3077 ÷ 41? (a) 770 (b) 77 (c) 7700
  7. 7.Best estimate of 1276 ÷ 26? (a) 43 (b) 430 (c) 4300
  8. 8.Best estimate of 2016 ÷ 63? (a) 3400 (b) 340 (c) 34
  9. 9.Best estimate of 5712 ÷ 88? (a) 630 (b) 6300 (c) 63
  10. 10.√35 to 1 decimal place? (a) 5.6 (b) 5.7 (c) 5.8 (d) 5.9
  11. 11.Best estimate of 603 ÷ 43? (a) 15 (b) 1500 (c) 150
  12. 12.√20 to 1 decimal place? (a) 4.7 (b) 4.5 (c) 4.8 (d) 4.6
  13. 13.√24 to 1 decimal place? (a) 5.0 (b) 5.1 (c) 5.2 (d) 4.9
  14. 14.Best estimate of 5859 ÷ 62? (a) 980 (b) 98 (c) 9800
  15. 15.√50 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 7.1 (d) 6.8
  16. 16.√63 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 8.1 (d) 7.8
  17. 17.√21 to 1 decimal place? (a) 4.7 (b) 4.5 (c) 4.6 (d) 4.4
  18. 18.Best estimate of 1128 ÷ 33? (a) 38 (b) 3800 (c) 380
  19. 19.Best estimate of 3495 ÷ 61? (a) 5800 (b) 58 (c) 580
  20. 20.Best estimate of 4304 ÷ 87? (a) 48 (b) 480 (c) 4800
  21. 21.Best estimate of 1859 ÷ 62? (a) 310 (b) 3100 (c) 31
  22. 22.Best estimate of 779 ÷ 34? (a) 26 (b) 260 (c) 2600
  23. 23.√92 to 1 decimal place? (a) 9.9 (b) 9.8 (c) 9.6 (d) 9.7
  24. 24.Best estimate of 1212 ÷ 48? (a) 24 (b) 2400 (c) 240
  25. 25.Best estimate of 4455 ÷ 72? (a) 640 (b) 6400 (c) 64
  26. 26.Best estimate of 2507 ÷ 49? (a) 5000 (b) 500 (c) 50
  27. 27.√38 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.5 (d) 6.2
  28. 28.Best estimate of 5706 ÷ 62? (a) 9500 (b) 950 (c) 95
  29. 29.√44 to 1 decimal place? (a) 6.5 (b) 6.7 (c) 6.6 (d) 6.4
  30. 30.Best estimate of 1231 ÷ 46? (a) 250 (b) 25 (c) 2500
  31. 31.Best estimate of 3846 ÷ 62? (a) 640 (b) 6400 (c) 64
  32. 32.√61 to 1 decimal place? (a) 7.5 (b) 7.7 (c) 7.6 (d) 7.8
  33. 33.Best estimate of 1371 ÷ 64? (a) 23 (b) 230 (c) 2300
  34. 34.Best estimate of 3366 ÷ 52? (a) 670 (b) 67 (c) 6700
  35. 35.Best estimate of 5062 ÷ 72? (a) 720 (b) 7200 (c) 72
  36. 36.√77 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.5 (d) 8.8
  37. 37.√48 to 1 decimal place? (a) 7.0 (b) 7.2 (c) 7.1 (d) 6.9
  38. 38.Best estimate of 4858 ÷ 88? (a) 540 (b) 54 (c) 5400
  39. 39.√55 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.7 (d) 7.4
  40. 40.Best estimate of 1656 ÷ 42? (a) 410 (b) 41 (c) 4100

Answer key

  1. 5.2
  2. 74
  3. 9.2
  4. 55
  5. 8.3
  6. 77
  7. 43
  8. 34
  9. 63
  10. 5.9
  11. 15
  12. 4.5
  13. 4.9
  14. 98
  15. 7.1
  16. 7.9
  17. 4.6
  18. 38
  19. 58
  20. 48
  21. 31
  22. 26
  23. 9.6
  24. 24
  25. 64
  26. 50
  27. 6.2
  28. 95
  29. 6.6
  30. 25
  31. 64
  32. 7.8
  33. 23
  34. 67
  35. 72
  36. 8.8
  37. 6.9
  38. 54
  39. 7.4
  40. 41

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