To determine which integers are perfect squares and which are not, we need to check if each number can be expressed as the square of some integer. Here is the step-by-step categorization of the given integers:
1. 6
- To check if 6 is a perfect square, we look for an integer [tex]\( n \)[/tex] such that [tex]\( n^2 = 6 \)[/tex].
- [tex]\( \sqrt{6} \)[/tex] is approximately 2.45, which is not an integer.
- Therefore, 6 is a non-perfect square.
2. 9
- To check if 9 is a perfect square, we look for an integer [tex]\( n \)[/tex] such that [tex]\( n^2 = 9 \)[/tex].
- [tex]\( \sqrt{9} = 3 \)[/tex], which is an integer.
- Therefore, 9 is a perfect square.
3. 88
- To check if 88 is a perfect square, we look for an integer [tex]\( n \)[/tex] such that [tex]\( n^2 = 88 \)[/tex].
- [tex]\( \sqrt{88} \)[/tex] is approximately 9.38, which is not an integer.
- Therefore, 88 is a non-perfect square.
4. 64
- To check if 64 is a perfect square, we look for an integer [tex]\( n \)[/tex] such that [tex]\( n^2 = 64 \)[/tex].
- [tex]\( \sqrt{64} = 8 \)[/tex], which is an integer.
- Therefore, 64 is a perfect square.
5. 24
- To check if 24 is a perfect square, we look for an integer [tex]\( n \)[/tex] such that [tex]\( n^2 = 24 \)[/tex].
- [tex]\( \sqrt{24} \)[/tex] is approximately 4.89, which is not an integer.
- Therefore, 24 is a non-perfect square.
6. 49
- To check if 49 is a perfect square, we look for an integer [tex]\( n \)[/tex] such that [tex]\( n^2 = 49 \)[/tex].
- [tex]\( \sqrt{49} = 7 \)[/tex], which is an integer.
- Therefore, 49 is a perfect square.
Categorizing the numbers, we get:
- Perfect Squares: 9, 64, 49
- Non-Perfect Squares: 6, 88, 24
So, the sorted categories are:
- Perfect Squares: 9, 64, 49
- Non-Perfect Squares: 6, 88, 24
