Question

Which of the following is a rational number?(1 point)
Responses

7–√
square root of 7

7.8
7.8

88√
the fraction with numerator 8 and denominator square root of 8

π

Answer 1

sooooo?

Answer 2

A rational number is defined as a number that can be expressed as the quotient or fraction \( \frac{p}{q} \) of two integers, where \( p \) is an integer and \( q \) is a non-zero integer.

Now let's analyze each option:

1. **7 – √7**: This is not a rational number because it involves the square root of 7, which is an irrational number. The subtraction of a rational number (7) and an irrational number (√7) results in an irrational number.

2. **7.8**: This is a rational number because it can be expressed as \( \frac{78}{10} \).

3. **8/√8**: While this fraction may imply that it could be rational, it actually simplifies to \( 8/\sqrt{8} = 8 \times \frac{\sqrt{8}}{8} = \sqrt{8} \), which is irrational (since √8 is not a perfect square).

4. **π**: This is well-known to be an irrational number.

Out of the options provided, **7.8** is the only rational number.

Answer 3

The answer is **7.8**, which is a rational number. It can be expressed as a fraction, specifically \( \frac{78}{10} \), which meets the criteria for rational numbers. If you have any more questions or if there's anything else you'd like to know, feel free to ask!