# Is 128 a perfect cube. Find its cube root

To know whether the number is perfect cube or not, we have to use prime factorisation method

A method in which we write the original number as a product of various prime numbers is called prime factorisation

Therefore,

128 can be written as,

128 = 2 x 2 x 2 x 2 x 2 x 2 x 2

128 = (2 x 2 x 2) x (2 x 2 x 2) x 2

$$\sqrt[3]{128} = \left ( 2^{3}\times 2^{3}\times 2\right )^{\frac{1}{3}}\\= 2 \times 2\times 2^{\frac{1}{3}}$$

We get,

$$\sqrt[3]{128} = 4\sqrt[3]{2}$$

Hence, 128 is not a perfect cube and the cube root of 128 is $$4\sqrt[3]{2}$$