Determine whether the simplified expression is rational or irrational  _6+4(5)+5

To determine whether the expression is rational or irrational, we first need to simplify it. 

Let's evaluate the expression step by step:

\[
6 + 4 \cdot 5 + 5
\]

1. **Calculate the multiplication:**

\[
4 \cdot 5 = 20
\]

2. **Substitute and simplify the expression:**

\[
6 + 20 + 5
\]

3. **Add the numbers together:**

\[
6 + 20 + 5 = 31
\]

The result is **31**, which is a whole number. Since a whole number is a rational number (it can be expressed as the ratio of two integers, \(31 = \frac{31}{1}\)), the expression simplifies to a rational number.

### Conclusion
The simplified expression is **rational**.

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Would you like more details or have any questions? Here are some related questions to consider:

1. What is the definition of a rational number?
2. How do you determine if an expression involving square roots is rational or irrational?
3. What makes a number irrational?
4. Can fractions always be considered rational?
5. How do you simplify more complex algebraic expressions?

**Tip:** Remember, an expression is rational if it can be written as a fraction of two integers.

Learn how to determine if the expression 6 + 4(5) + 5 is rational or irrational through simplification. This problem involves basic arithmetic operations and understanding rational numbers. Suitable for students in Grades 5-6.

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