Question

Find the cube root of the following number.

729

Answer 1

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.