https://file.aiquickdraw.com/mathbot/file/1729794823157yb5zfzki.jpg

Let's break down each statement in the problem and determine whether it is true or false:

1. **"Since it is a ratio of two integers, \( \frac{2}{6} \) is rational."**
   - True: A rational number is any number that can be expressed as the ratio of two integers. \( \frac{2}{6} = \frac{1}{3} \), which is rational.

2. **"Since it is a terminating decimal, 7.9 is irrational."**
   - False: A terminating decimal is always rational. 7.9 can be expressed as \( \frac{79}{10} \), which makes it rational.

3. **"Since 13 is not a perfect square, \( \sqrt{13} \) is rational."**
   - False: \( \sqrt{13} \) is irrational because 13 is not a perfect square. Only the square roots of perfect squares are rational.

4. **"Since 25 is a perfect square, \( \sqrt{25} \) is rational."**
   - True: \( \sqrt{25} = 5 \), which is a rational number because 25 is a perfect square.

5. **"Since it is an integer, 13 is irrational."**
   - False: All integers are rational numbers because they can be expressed as a ratio (e.g., \( \frac{13}{1} \)).

6. **"None of the above statements are true."**
   - False: As we've already determined, some statements are true.

### Correct Answers:
- \( \frac{2}{6} \) is rational.
- \( \sqrt{25} \) is rational.

Would you like further details on any of these statements?

### Related Questions:
1. What makes a number rational or irrational?
2. Why are terminating decimals always rational?
3. Can a non-perfect square have a rational square root?
4. How can you express any integer as a rational number?
5. What is the difference between terminating and repeating decimals in terms of rationality?

### Tip:
When in doubt, remember that all integers and fractions are rational, and square roots of non-perfect squares are irrational.

Check all statements that are true about rational and irrational numbers, including whether fractions, square roots, and integers are rational or irrational.

Analyze various mathematical statements to determine if numbers, including fractions like 2/6, terminating decimals, and square roots of perfect and non-perfect squares, are rational or irrational. This problem is suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation