Cube Roots 1 to 99 (A) - Free Printable

To solve the problem of finding the cube roots of the given numbers, we need to determine which number, when multiplied by itself three times, equals the given number. Here's how we can approach each calculation:

General Approach:

1. Estimation: Start by estimating the cube root based on known cubes (e.g., \(1^3 = 1\), \(2^3 = 8\), \(3^3 = 27\), etc.).
2. Trial and Error or Calculation: Use a calculator or manual computation to refine the estimate.
3. Verification: Ensure that the cube of the calculated root equals the original number.

Detailed Solutions:

#### 1. \(\sqrt[3]{512}\)
- Estimation: \(8^3 = 512\)
- Verification: \(8 \times 8 \times 8 = 512\)
- Answer: \(8\)

#### 2. \(\sqrt[3]{512000}\)
- Estimation: \(80^3 = 512000\) (since \(8^3 = 512\) and adding two zeros suggests multiplying by \(10^3\))
- Verification: \(80 \times 80 \times 80 = 512000\)
- Answer: \(80\)

#### 3. \(\sqrt[3]{2197}\)
- Estimation: \(13^3 = 2197\) (since \(13 \times 13 \times 13 = 2197\))
- Verification: \(13 \times 13 \times 13 = 2197\)
- Answer: \(13\)

#### 4. \(\sqrt[3]{8}\)
- Estimation: \(2^3 = 8\)
- Verification: \(2 \times 2 \times 2 = 8\)
- Answer: \(2\)

#### 5. \(\sqrt[3]{166375}\)
- Estimation: \(55^3 = 166375\) (since \(55 \times 55 \times 55 = 166375\))
- Verification: \(55 \times 55 \times 55 = 166375\)
- Answer: \(55\)

#### 6. \(\sqrt[3]{592704}\)
- Estimation: \(84^3 = 592704\) (since \(84 \times 84 \times 84 = 592704\))
- Verification: \(84 \times 84 \times 84 = 592704\)
- Answer: \(84\)

#### 7. \(\sqrt[3]{456533}\)
- Estimation: \(77^3 = 456533\) (since \(77 \times 77 \times 77 = 456533\))
- Verification: \(77 \times 77 \times 77 = 456533\)
- Answer: \(77\)

#### 8. \(\sqrt[3]{328509}\)
- Estimation: \(69^3 = 328509\) (since \(69 \times 69 \times 69 = 328509\))
- Verification: \(69 \times 69 \times 69 = 328509\)
- Answer: \(69\)

#### 9. \(\sqrt[3]{493039}\)
- Estimation: \(79^3 = 493039\) (since \(79 \times 79 \times 79 = 493039\))
- Verification: \(79 \times 79 \times 79 = 493039\)
- Answer: \(79\)

#### 10. \(\sqrt[3]{2744}\)
- Estimation: \(14^3 = 2744\) (since \(14 \times 14 \times 14 = 2744\))
- Verification: \(14 \times 14 \times 14 = 2744\)
- Answer: \(14\)

#### 11. \(\sqrt[3]{857375}\)
- Estimation: \(95^3 = 857375\) (since \(95 \times 95 \times 95 = 857375\))
- Verification: \(95 \times 95 \times 95 = 857375\)
- Answer: \(95\)

#### 12. \(\sqrt[3]{39304}\)
- Estimation: \(34^3 = 39304\) (since \(34 \times 34 \times 34 = 39304\))
- Verification: \(34 \times 34 \times 34 = 39304\)
- Answer: \(34\)

#### 13. \(\sqrt[3]{8000}\)
- Estimation: \(20^3 = 8000\) (since \(20 \times 20 \times 20 = 8000\))
- Verification: \(20 \times 20 \times 20 = 8000\)
- Answer: \(20\)

#### 14. \(\sqrt[3]{405224}\)
- Estimation: \(74^3 = 405224\) (since \(74 \times 74 \times 74 = 405224\))
- Verification: \(74 \times 74 \times 74 = 405224\)
- Answer: \(74\)

#### 15. \(\sqrt[3]{132651}\)
- Estimation: \(51^3 = 132651\) (since \(51 \times 51 \times 51 = 132651\))
- Verification: \(51 \times 51 \times 51 = 132651\)
- Answer: \(51\)

#### 16. \(\sqrt[3]{4913}\)
- Estimation: \(17^3 = 4913\) (since \(17 \times 17 \times 17 = 4913\))
- Verification: \(17 \times 17 \times 17 = 4913\)
- Answer: \(17\)

#### 17. \(\sqrt[3]{753571}\)
- Estimation: \(91^3 = 753571\) (since \(91 \times 91 \times 91 = 753571\))
- Verification: \(91 \times 91 \times 91 = 753571\)
- Answer: \(91\)

#### 18. \(\sqrt[3]{29791}\)
- Estimation: \(31^3 = 29791\) (since \(31 \times 31 \times 31 = 29791\))
- Verification: \(31 \times 31 \times 31 = 29791\)
- Answer: \(31\)

#### 19. \(\sqrt[3]{97336}\)
- Estimation: \(46^3 = 97336\) (since \(46 \times 46 \times 46 = 97336\))
- Verification: \(46 \times 46 \times 46 = 97336\)
- Answer: \(46\)

#### 20. \(\sqrt[3]{175616}\)
- Estimation: \(56^3 = 175616\) (since \(56 \times 56 \times 56 = 175616\))
- Verification: \(56 \times 56 \times 56 = 175616\)
- Answer: \(56\)

#### 21. \(\sqrt[3]{54872}\)
- Estimation: \(38^3 = 54872\) (since \(38 \times 38 \times 38 = 54872\))
- Verification: \(38 \times 38 \times 38 = 54872\)
- Answer: \(38\)

#### 22. \(\sqrt[3]{13824}\)
- Estimation: \(24^3 = 13824\) (since \(24 \times 24 \times 24 = 13824\))
- Verification: \(24 \times 24 \times 24 = 13824\)
- Answer: \(24\)

#### 23. \(\sqrt[3]{117649}\)
- Estimation: \(49^3 = 117649\) (since \(49 \times 49 \times 49 = 117649\))
- Verification: \(49 \times 49 \times 49 = 117649\)
- Answer: \(49\)

#### 24. \(\sqrt[3]{205379}\)
- Estimation: \(59^3 = 205379\) (since \(59 \times 59 \times 59 = 205379\))
- Verification: \(59 \times 59 \times 59 = 205379\)
- Answer: \(59\)

#### 25. \(\sqrt[3]{551368}\)
- Estimation: \(82^3 = 551368\) (since \(82 \times 82 \times 82 = 551368\))
- Verification: \(82 \times 82 \times 82 = 551368\)
- Answer: \(82\)

#### 26. \(\sqrt[3]{15625}\)
- Estimation: \(25^3 = 15625\) (since \(25 \times 25 \times 25 = 15625\))
- Verification: \(25 \times 25 \times 25 = 15625\)
- Answer: \(25\)

#### 27. \(\sqrt[3]{474552}\)
- Estimation: \(78^3 = 474552\) (since \(78 \times 78 \times 78 = 474552\))
- Verification: \(78 \times 78 \times 78 = 474552\)
- Answer: \(78\)

#### 28. \(\sqrt[3]{226981}\)
- Estimation: \(61^3 = 226981\) (since \(61 \times 61 \times 61 = 226981\))
- Verification: \(61 \times 61 \times 61 = 226981\)
- Answer: \(61\)

#### 29. \(\sqrt[3]{884736}\)
- Estimation: \(96^3 = 884736\) (since \(96 \times 96 \times 96 = 884736\))
- Verification: \(96 \times 96 \times 96 = 884736\)
- Answer: \(96\)

#### 30. \(\sqrt[3]{125}\)
- Estimation: \(5^3 = 125\) (since \(5 \times 5 \times 5 = 125\))
- Verification: \(5 \times 5 \times 5 = 125\)
- Answer: \(5\)

Final Answers:

\[
\boxed{
\begin{array}{ccc}
\sqrt[3]{512} = 8 & \sqrt[3]{512000} = 80 & \sqrt[3]{2197} = 13 \\
\sqrt[3]{8} = 2 & \sqrt[3]{166375} = 55 & \sqrt[3]{592704} = 84 \\
\sqrt[3]{456533} = 77 & \sqrt[3]{328509} = 69 & \sqrt[3]{493039} = 79 \\
\sqrt[3]{2744} = 14 & \sqrt[3]{857375} = 95 & \sqrt[3]{39304} = 34 \\
\sqrt[3]{8000} = 20 & \sqrt[3]{405224} = 74 & \sqrt[3]{132651} = 51 \\
\sqrt[3]{4913} = 17 & \sqrt[3]{753571} = 91 & \sqrt[3]{29791} = 31 \\
\sqrt[3]{97336} = 46 & \sqrt[3]{175616} = 56 & \sqrt[3]{54872} = 38 \\
\sqrt[3]{13824} = 24 & \sqrt[3]{117649} = 49 & \sqrt[3]{205379} = 59 \\
\sqrt[3]{551368} = 82 & \sqrt[3]{15625} = 25 & \sqrt[3]{474552} = 78 \\
\sqrt[3]{226981} = 61 & \sqrt[3]{884736} = 96 & \sqrt[3]{125} = 5 \\
\end{array}
}
\]