Answer :
To determine which of the given numbers is a perfect square, we need to recall that a perfect square is an integer that can be expressed as the square of another integer.
Let’s analyze each option step-by-step:
A) 100
To check if 100 is a perfect square, we need to find if there is an integer [tex]\( n \)[/tex] such that [tex]\( n^2 = 100 \)[/tex].
- [tex]\( 10^2 = 100 \)[/tex].
- Therefore, 100 is a perfect square.
B) 13
To check if 13 is a perfect square, we need to find if there is an integer [tex]\( n \)[/tex] such that [tex]\( n^2 = 13 \)[/tex].
- The square root of 13 is approximately 3.605, which is not an integer.
- Therefore, 13 is not a perfect square.
C) 102
To check if 102 is a perfect square, we need to find if there is an integer [tex]\( n \)[/tex] such that [tex]\( n^2 = 102 \)[/tex].
- The square root of 102 is approximately 10.1, which is not an integer.
- Therefore, 102 is not a perfect square.
D) 127
To check if 127 is a perfect square, we need to find if there is an integer [tex]\( n \)[/tex] such that [tex]\( n^2 = 127 \)[/tex].
- The square root of 127 is approximately 11.27, which is not an integer.
- Therefore, 127 is not a perfect square.
Based on our analysis, the only number among the options that is a perfect square is [tex]\( \boxed{100} \)[/tex].
Let’s analyze each option step-by-step:
A) 100
To check if 100 is a perfect square, we need to find if there is an integer [tex]\( n \)[/tex] such that [tex]\( n^2 = 100 \)[/tex].
- [tex]\( 10^2 = 100 \)[/tex].
- Therefore, 100 is a perfect square.
B) 13
To check if 13 is a perfect square, we need to find if there is an integer [tex]\( n \)[/tex] such that [tex]\( n^2 = 13 \)[/tex].
- The square root of 13 is approximately 3.605, which is not an integer.
- Therefore, 13 is not a perfect square.
C) 102
To check if 102 is a perfect square, we need to find if there is an integer [tex]\( n \)[/tex] such that [tex]\( n^2 = 102 \)[/tex].
- The square root of 102 is approximately 10.1, which is not an integer.
- Therefore, 102 is not a perfect square.
D) 127
To check if 127 is a perfect square, we need to find if there is an integer [tex]\( n \)[/tex] such that [tex]\( n^2 = 127 \)[/tex].
- The square root of 127 is approximately 11.27, which is not an integer.
- Therefore, 127 is not a perfect square.
Based on our analysis, the only number among the options that is a perfect square is [tex]\( \boxed{100} \)[/tex].
