Answer:
Explanation:
To show that a number is not a perfect square, we need to demonstrate that it cannot be expressed as the product of two equal integers.
1. 27: The prime factorization of 27 is 3 x 3 x 3. Since there are no pairs of equal factors, 27 is not a perfect square.
2. 81: The prime factorization of 81 is 3 x 3 x 3 x 3. Again, there are no pairs of equal factors, so 81 is not a perfect square.
3. 13: This number is a prime number, which means it cannot be expressed as the product of two smaller integers. Therefore, 13 is not a perfect square.
4. 48: The prime factorization of 48 is 2 x 2 x 2 x 2 x 3. Notice that there is only one pair of equal factors (2 x 2), but there is also a factor of 3. Therefore, 48 is not a perfect square.
5. 101: This number is also a prime number, and therefore it cannot be expressed as the product of two smaller integers. Hence, 101 is not a perfect square.