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.
Similar Questions
- Which of these is both an Integer and a Whole number?
- Which of the following is a non-zero number that belongs to every set: Whole, Integer, Rational, and Real?
- What is the smallest number that must be added to 2378 to make it a perfect square?
- The set of real numbers includes which of the following?
In the following examples, a number is coded as three digits — representing the remainders when the number is divided by 3, 7, and 11, respectively.
Example 1: $53 \rightarrow 53 \div 3 = 17 \text{ R} 2$, $53 \div 7 = 7 \text{ R } 4$, $53 \div 11 = 4 \text{ R } 9 \rightarrow \text{ Code: } 2, 4, 9$
Example 2: $68 \rightarrow 68 \div 3 = 22 \text{ R} 2$, $68 \div 7 = 9 \text{ R } 5$, $68 \div 11 = 6 \text{ R } 2 \rightarrow \text{ Code: } 2, 5, 2$
By following this method, which is the least number which would have the code - 2, 2, 2?- Which roll number has only prime digits?
- A student was asked to find the sum of first 20 odd numbers. His answer was 400. Correct?
- Which roll number is a perfect cube?
- Which roll number has a digital root equal to 9? Digital root = sum of digits until one digit remains.
Which of the following statement is TRUE for Whole Numbers?
Important Questions from Number System
Consider the following statements :
1. (25)! + 1 is divisible by 26
2. (6)! + 1 is divisible by 7
Which of the above statements is/are correct ?
If the sum S is divided by 8, what is the remainder ?
If the sum S is divided by 60, what is the remainder ?
Find the sum of squares of the greatest value and the smallest value of K in the number so that the number 45082K is divisible by 3.
How many composite numbers are there from 53 to 97 ?
