Identify Perfect Square and Integer Value

This solution explains how to find the option that represents a number meeting the criteria of being both a perfect square and an integer.

Key Definitions

• Integer: A whole number, including positive numbers, negative numbers, and zero (e.g., $ -2 $, $ 0 $, $ 7 $).
• Perfect Square: An integer that is the result of squaring another integer (e.g., $ 9 $ is a perfect square because $ 9 = 3^2 $). The sequence starts $ 0, 1, 4, 9, 16, \dots $.

The question requires identifying an option whose value is an integer and, if applicable, is derived from a perfect square. Based on the options, we interpret this as the resulting value must be an integer, and the number under the square root symbol must itself be a perfect square.

Option Analysis

• Option 1: $Square root of 5$
  • Value: $ \sqrt{5} \approx 2.236 $
  • Is it an integer? No.
  • Is 5 a perfect square? No.
  • This option does not meet the criteria.
• Option 2: $Square root of 9$
  • Value: $ \sqrt{9} = 3 $
  • Is the value an integer? Yes.
  • Is 9 (the number under the radical) a perfect square? Yes, $ 9 = 3^2 $.
  • This option meets the criteria.
• Option 3: $3.2$
  • Is it an integer? No.
  • This option does not meet the criteria.
• Option 4: $3.4$
  • Is it an integer? No.
  • This option does not meet the criteria.
• Option 5: (Empty)
  • No value provided.
  • This option does not meet the criteria.

Final Answer Determination

The analysis shows that $Square root of 9$ evaluates to $ 3 $. The number $ 3 $ is an integer, and $ 9 $ is a perfect square. Therefore, this option satisfies the conditions.