Answer :
To determine which statement justifies that 169 is a perfect square, let’s analyze each option:
A. [tex]\(\frac{169}{2} = 84.5\)[/tex]
This statement calculates half of 169. It doesn't provide any information regarding whether 169 is a perfect square since it just expresses 169 as a fraction.
B. [tex]\(100 + 69 = 169\)[/tex]
This statement simply adds up two numbers to get 169, but it doesn't tell us anything about whether 169 can be expressed as the product of an integer with itself.
C. [tex]\(2 \cdot 13 = 169\)[/tex]
This statement is incorrect mathematically. Multiplying 2 by 13 gives 26, not 169. Therefore, this statement does not help in determining if 169 is a perfect square.
D. [tex]\(13 \cdot 13 = 169\)[/tex]
This statement correctly shows that multiplying 13 by itself gives 169. This is the definition of a perfect square, where a number can be expressed as the product of an integer by itself. Since [tex]\(13 \cdot 13 = 169\)[/tex], it demonstrates that 169 is indeed a perfect square.
Therefore, the correct statement that justifies 169 as a perfect square is:
D. [tex]\(13 \cdot 13 = 169\)[/tex]
A. [tex]\(\frac{169}{2} = 84.5\)[/tex]
This statement calculates half of 169. It doesn't provide any information regarding whether 169 is a perfect square since it just expresses 169 as a fraction.
B. [tex]\(100 + 69 = 169\)[/tex]
This statement simply adds up two numbers to get 169, but it doesn't tell us anything about whether 169 can be expressed as the product of an integer with itself.
C. [tex]\(2 \cdot 13 = 169\)[/tex]
This statement is incorrect mathematically. Multiplying 2 by 13 gives 26, not 169. Therefore, this statement does not help in determining if 169 is a perfect square.
D. [tex]\(13 \cdot 13 = 169\)[/tex]
This statement correctly shows that multiplying 13 by itself gives 169. This is the definition of a perfect square, where a number can be expressed as the product of an integer by itself. Since [tex]\(13 \cdot 13 = 169\)[/tex], it demonstrates that 169 is indeed a perfect square.
Therefore, the correct statement that justifies 169 as a perfect square is:
D. [tex]\(13 \cdot 13 = 169\)[/tex]
