State whether the given statement is true or false.

243 is a perfect cube.

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True

False

answer is B.

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Detailed Solution

The given statement is false.
Concept- In this question, we are given a number and asked to determine whether or not it is a perfect cube. In addition, we were asked if it is a perfect cube, and if so, whose perfect cube it is. Find the prime factors of the number first, and then form groups of triplets of prime factors. If the triplets are formed, the number is a perfect cube; otherwise, it is not. If it is a perfect cube, multiply one of the triplet numbers by the other triplet number. Repeat this process until all of the triplets have been considered, and you will have the needed number.
A perfect cube can be expressed as a product of three same numbers
Now, find prime factor of the given number we get,

As given no. has more than three factors or we can say that prime factors can’t be grouped into pairs of three same nos.
Therefore, “243 is not a perfect cube”, would be the right statement.
Hence, the given statement is false.

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