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Question
Find the cube root of the following number.
729
Solution
To find the cube root of 729, let us factorise 729 first.
| 3 | 729 |
| 3 | 243 |
| 3 | 81 |
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
729 = 3 × 3 × 3 × 3 × 3 × 3
\[\sqrt[3]{729} = \sqrt[3]{3\times3\times3\times3\times3\times3}\]
\[\Rightarrow\sqrt[3]{729} = \sqrt[3]{{(3\times3\times3)}\times{(3\times3\times3)}}\]
\[\Rightarrow\sqrt[3]{729} = 3\times3\]
\[\Rightarrow\sqrt[3]{729} = 9\]
Hence, the cube root of 729 is 9.
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