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

Question

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