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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 505 · 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.√69 to 1 decimal place? (a) 8.5 (b) 8.3 (c) 8.6 (d) 8.4
  2. 2.√27 to 1 decimal place? (a) 5.0 (b) 5.3 (c) 5.2 (d) 5.1
  3. 3.Best estimate of 4172 ÷ 44? (a) 1040 (b) 104 (c) 10400
  4. 4.√78 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.6 (d) 8.5
  5. 5.Best estimate of 2730 ÷ 87? (a) 30 (b) 300 (c) 3000
  6. 6.√41 to 1 decimal place? (a) 6.7 (b) 6.4 (c) 6.5 (d) 6.6
  7. 7.Best estimate of 514 ÷ 21? (a) 260 (b) 2600 (c) 26
  8. 8.Best estimate of 516 ÷ 26? (a) 1700 (b) 17 (c) 170
  9. 9.Best estimate of 2612 ÷ 72? (a) 37 (b) 3700 (c) 370
  10. 10.√30 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.6 (d) 5.3
  11. 11.√37 to 1 decimal place? (a) 6.2 (b) 5.9 (c) 6.1 (d) 6.0
  12. 12.Best estimate of 992 ÷ 34? (a) 33 (b) 3300 (c) 330
  13. 13.Best estimate of 1259 ÷ 46? (a) 250 (b) 2500 (c) 25
  14. 14.Best estimate of 2822 ÷ 32? (a) 94 (b) 940 (c) 9400
  15. 15.√92 to 1 decimal place? (a) 9.8 (b) 9.5 (c) 9.6 (d) 9.7
  16. 16.Best estimate of 3290 ÷ 63? (a) 55 (b) 550 (c) 5500
  17. 17.Best estimate of 1286 ÷ 78? (a) 1600 (b) 16 (c) 160
  18. 18.Best estimate of 7319 ÷ 86? (a) 8100 (b) 81 (c) 810
  19. 19.Best estimate of 5252 ÷ 56? (a) 8800 (b) 880 (c) 88
  20. 20.Best estimate of 2438 ÷ 44? (a) 610 (b) 6100 (c) 61
  21. 21.Best estimate of 2655 ÷ 36? (a) 6600 (b) 66 (c) 660
  22. 22.Best estimate of 2927 ÷ 37? (a) 730 (b) 7300 (c) 73
  23. 23.Best estimate of 2473 ÷ 82? (a) 310 (b) 3100 (c) 31
  24. 24.√66 to 1 decimal place? (a) 7.8 (b) 8.0 (c) 7.9 (d) 8.1
  25. 25.√74 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.7 (d) 8.9
  26. 26.Best estimate of 425 ÷ 26? (a) 140 (b) 1400 (c) 14
  27. 27.Best estimate of 1610 ÷ 52? (a) 3200 (b) 320 (c) 32
  28. 28.Best estimate of 3855 ÷ 63? (a) 640 (b) 6400 (c) 64
  29. 29.Best estimate of 2654 ÷ 52? (a) 5300 (b) 53 (c) 530
  30. 30.Best estimate of 1188 ÷ 39? (a) 30 (b) 3000 (c) 300
  31. 31.√38 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.0 (d) 6.1
  32. 32.√32 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 5.6 (d) 5.7
  33. 33.Best estimate of 2432 ÷ 29? (a) 81 (b) 8100 (c) 810
  34. 34.√67 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 8.2 (d) 8.3
  35. 35.Best estimate of 1300 ÷ 21? (a) 65 (b) 6500 (c) 650
  36. 36.√71 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.6 (d) 8.5
  37. 37.Best estimate of 3769 ÷ 48? (a) 750 (b) 7500 (c) 75
  38. 38.Best estimate of 4970 ÷ 86? (a) 550 (b) 55 (c) 5500
  39. 39.Best estimate of 6229 ÷ 69? (a) 8900 (b) 89 (c) 890
  40. 40.√40 to 1 decimal place? (a) 6.2 (b) 6.5 (c) 6.3 (d) 6.4

Answer key

  1. 8.3
  2. 5.2
  3. 104
  4. 8.8
  5. 30
  6. 6.4
  7. 26
  8. 17
  9. 37
  10. 5.5
  11. 6.1
  12. 33
  13. 25
  14. 94
  15. 9.6
  16. 55
  17. 16
  18. 81
  19. 88
  20. 61
  21. 66
  22. 73
  23. 31
  24. 8.1
  25. 8.6
  26. 14
  27. 32
  28. 64
  29. 53
  30. 30
  31. 6.2
  32. 5.7
  33. 81
  34. 8.2
  35. 65
  36. 8.4
  37. 75
  38. 55
  39. 89
  40. 6.3

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