Question 11 Mark
Is $68600$ a perfect cube$?$ If not, find the smallest number by which 68600 must be multiplied to get a perfect cube$?$
Answer
View full question & answer→We have, $68600 = 2 \times 2 \times 2 \times 5 \times 5 \times 7 \times 7 \times 7$. In this factorisation, we find that there is no triplet of $5.$
So, $68600$ is not a perfect cube. To make it a perfect cube we multiply it by $5.$
Thus, $68600 \times 5 = 2 \times 2 \times 2 \times 5 \times 5 \times 5 \times 7 \times 7 \times 7 = 343000,$ which is a perfect cube.
Hence, the smallest number by which $68600$ must be multiplied to get a perfect cube is $5.$
So, $68600$ is not a perfect cube. To make it a perfect cube we multiply it by $5.$
Thus, $68600 \times 5 = 2 \times 2 \times 2 \times 5 \times 5 \times 5 \times 7 \times 7 \times 7 = 343000,$ which is a perfect cube.
Hence, the smallest number by which $68600$ must be multiplied to get a perfect cube is $5.$