Question

$$\begin{gathered} \text{Q}\text{.Find out the cube root of 216}\text{.} \\ \text{A}\text{. 8} \\ \text{B}\text{. 4} \\ \text{C}\text{. 9} \\ \text{D}\text{. 6} \end{gathered}$$

Answer 1

$$\begin{gathered} \text{In mathematics a cube root of a number }x\text{ is number }y\text{such that }{y}^3=x....\left(1\right) \\ \text{now finding the cube root of the number by prime factorization}\text{.} \\ \text{from the equation one } \\ {y}^3=216 \\ y=\sqrt[3]{216} \\ \text{prime factors of are } \\ \text{216 = 2}\times \text{2}\times \text{2}\times \text{3}\times \text{3}\times \text{3} \\ \text{now assume three time repeating digits as one}\text{.} \\ \text{as here by assuming each three as one we will get 2and 3}\text{.} \\ \text{now we should multiply these numbers}\text{.} \\ \text{2}\times \text{3 = 6 } \\ \sqrt[3]{216}=6 \\ \text{which is the cube root of 216 as mentioned}\text{.} \\ \text{NOTE: whenever you come across this kind of question find out the prime factors of the given number} \\ \text{ and always assume the three time repeating digit as one and multiply them to get the cube root } \\ \text{ of the number } \end{gathered}$$