Question

5 + \( \sqrt{7} \) is:

• A. an irrational number
• B. a rational number
• C. an integer
• D. a whole number

Hint:

The sum of a rational number and an irrational number is always irrational.

Answer 1

The Correct Option is A

We are given the expression \( 5 + \sqrt{7} \). We need to determine whether this is a rational or irrational number.
- A rational number is any number that can be written as a ratio of two integers, i.e., \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \).
- An irrational number is a number that cannot be written as a simple fraction, such as \( \sqrt{2} \), \( \pi \), and \( \sqrt{7} \), since these numbers cannot be expressed as a ratio of two integers.
Step 1: We know that \( \sqrt{7} \) is an irrational number.
Step 2: Adding a rational number (5) to an irrational number (\( \sqrt{7} \)) results in an irrational number. Hence, \( 5 + \sqrt{7} \) is irrational.
Thus, \( 5 + \sqrt{7} \) is an irrational number.