State whether the given statement is true or false.

9261 a perfect cube.

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True

False

answer is A.

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Detailed Solution

The given statement is true.
Concept- 1) A cube is a number which is a product of three identical numbers. e.g.

is a cube of 5 or write it as the third power of a no. or we can say that cube is the no. which is multiplied by its square: e.g.

2) A perfect cube is an integer's cube.
3) It can be noted that

and

implies 9261 be the cube of some no. between 20 and 30 most probably we can say that it is nearest to 20 .
4) The powers of all prime numbers in the prime-factorization of a cube are multiples of 3 .
To discover if 9261 is a cube or not, let's factor it into prime factors.
Here, we see that 9261 is not divisible by 2 or 5 but it is a multiple of 3. So, divide 9261 by 3.

3087 can be divided by 3 again.

Finally, after several rounds of division by prime integers, we arrive at the factorization shown below:

Which can be written as:

Due to the fact that all prime number powers are multiples of three, the number 9261 is a perfect cube.
Also,

.
So, 9261 is the cube of 21 .
Hence, the given statement is true.

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