A 5-digit number is a perfect cube as well as a perfect square. When the number is divided by 4, the result is a perfect square but not a perfect cube. When the number is divided by 27, the result is a perfect cube but not a perfect square. Find the number.
Answers
Answer:
There are two ways to interpret this question, namely:
You want to know a number which can act as the perfect square root as well as the perfect cube root.
You want to know a number which is a perfect square as well as a perfect cube of an integer.
In the first case, the solution is simple. Any non-negative integer is a perfect square root as well as a perfect cube root of a larger number.
A non-negative integer, say 0, is the perfect square root of 0 as well as a perfect cube root of 0. This holds true for all non-negative integers beginning from 0 i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,……….
In the second case too, the solution is simple but it entails a more logical approach than the first option.
A perfect square is a number which comprises of prime factors having powers which are a multiple of 2. Similarly, a perfect cube is a number which comprises of prime factors having powers which are a multiple of 3.
Any number which comprises of prime factors having powers which are a multiple of 6 will be the solution to your question; an example of which would be 64 which is the perfect square of 8 as well as a perfect cube of 4. In this case, the number 64 can be represented in the form of prime factors (i.e. 2^6) having powers (i.e. 6) which are a multiple of 6.
Answer:
5 is the answer.
Step-by-step explanation:
Hope it helps