Question

Determine whether each expression could be identified as rational or irrational. Select Rational or Irrational for each expression.


Expression Rational Irrational
5+7
√3 x 4
√7 + 2√7
1/5 + 4
-π + 4π

Answer 1

Let's evaluate each expression to determine if they are rational or irrational:

1. **5 + 7**
This is a simple arithmetic addition.
**Rational**

2. **√3 x 4**
This is the product of a rational number (4) and an irrational number (√3), which results in an irrational number.
**Irrational**

3. **√7 + 2√7**
This can be simplified to 3√7. Since √7 is irrational, the sum of an irrational number with itself multiplied by a rational number is also irrational.
**Irrational**

4. **1/5 + 4**
This adds a rational number (1/5) to another rational number (4). The sum of two rational numbers is rational.
**Rational**

5. **-π + 4π**
This simplifies to 3π. Since π is irrational, any non-zero rational multiple of π will also be irrational.
**Irrational**

So the summary is:

1. 5 + 7: **Rational**
2. √3 x 4: **Irrational**
3. √7 + 2√7: **Irrational**
4. 1/5 + 4: **Rational**
5. -π + 4π: **Irrational**