Questions: 0,4,9,64,144,169

Solution Steps

To determine which numbers are perfect squares, we need to check if each number in the list has an integer as its square root. A perfect square is a number that can be expressed as the product of an integer with itself.

We need to determine which numbers from the list \( \{0, 4, 8, 9, 15, 30, 42, 64, 72, 95, 144, 169\} \) are perfect squares. A perfect square is defined as a number that can be expressed as \( n^2 \) where \( n \) is an integer.

We check each number in the list:

• \( 0 = 0^2 \)
• \( 4 = 2^2 \)
• \( 8 \) is not a perfect square.
• \( 9 = 3^2 \)
• \( 15 \) is not a perfect square.
• \( 30 \) is not a perfect square.
• \( 42 \) is not a perfect square.
• \( 64 = 8^2 \)
• \( 72 \) is not a perfect square.
• \( 95 \) is not a perfect square.
• \( 144 = 12^2 \)
• \( 169 = 13^2 \)

From our checks, the perfect squares identified are \( 0, 4, 9, 64, 144, \) and \( 169 \).

Final Answer