. Without doing any calculations, answer the question:

Question

Would the result of this problem be a rational
number? Explain why or why not.
7.95 + √2

Answer 1

The expression given is \( 7.95 + \sqrt{2} \).

To determine if this result is a rational number, we need to consider the components of the expression:

1. \( 7.95 \) is a rational number because it can be expressed as the fraction \( \frac{795}{100} \).
2. \( \sqrt{2} \) is an irrational number, which means it cannot be expressed as a fraction of two integers.

When you add a rational number (like \( 7.95 \)) to an irrational number (like \( \sqrt{2} \)), the result is always irrational. This is because the sum of a rational and an irrational number cannot yield a number that can be expressed as a fraction of two integers.

Therefore, the result of \( 7.95 + \sqrt{2} \) would be an irrational number, not a rational number.