Question

Which of the following is not irrational?

• A. \( 5 - \sqrt{3} \)
• B. \( 7 - \sqrt{4} \)
• C. \( \sqrt{2} + \sqrt{3} \)
• D. \( \sqrt{2} - \sqrt{3} \)

Hint:

To identify irrational numbers, look for numbers involving square roots of non-perfect squares, as these are irrational.

Answer 1

The Correct Option is B

Step 1: Understand the concept of irrational numbers 
An irrational number is a number that cannot be expressed as a ratio of two integers, meaning its decimal form is non-terminating and non-repeating. Examples include \( \sqrt{2}, \sqrt{3}, \pi \), etc. A rational number is a number that can be expressed as the ratio of two integers. 
Step 2: Analyze each option
Option (1): \( 5 - \sqrt{3} \) is an irrational number because \( \sqrt{3} \) is irrational, and subtracting an irrational number from a rational number results in an irrational number.
Option (2): \( 7 - \sqrt{4} = 7 - 2 = 5 \), which is a rational number. Hence, this is not irrational.
Option (3): \( \sqrt{2} + \sqrt{3} \) is irrational, as the sum of two irrational numbers is usually irrational.
Option (4): \( \sqrt{2} - \sqrt{3} \) is also irrational, as the difference of two irrational numbers is typically irrational. 
Step 3: Conclusion
The only rational number is \( 7 - \sqrt{4} = 5 \), so the correct answer is option \( (2) \).