Insert two irrational numbers between 5 and 6.

Answer

To insert two irrational numbers between 5 and 6, we can follow these steps:

### Step 1: Identify the range
We need to find two irrational numbers that lie between 5 and 6.

### Step 2: Choose a base number
Let's start with a number between 5 and 6. We can choose 5.5 as a base point.

### Step 3: Create an irrational number
To create an irrational number, we can add a non-repeating, non-terminating decimal to our base number. For example, we can take the square root of a non-perfect square.

1. **First Irrational Number**:
- We can take \( \sqrt{2} \) which is approximately 1.414.
- Now, add this to 5:
\[ 5 + \sqrt{2} \approx 5 + 1.414 = 6.414 \]
- Since this is greater than 6, we can subtract instead:
\[ 5 + \sqrt{2} - 1 \approx 5 + 1.414 - 1 = 5.414 \]
- So, the first irrational number is \( 5 + \sqrt{2} - 1 \approx 5.414 \).

2. **Second Irrational Number**:
- Now, let's use \( \sqrt{3} \) which is approximately 1.732.
- Again, add this to 5:
\[ 5 + \sqrt{3} \approx 5 + 1.732 = 6.732 \]
- Since this is also greater than 6, we can subtract:
\[ 5 + \sqrt{3} - 1 \approx 5 + 1.732 - 1 = 5.732 \]
- So, the second irrational number is \( 5 + \sqrt{3} - 1 \approx 5.732 \).

### Conclusion
Thus, two irrational numbers between 5 and 6 are:
1. \( 5 + \sqrt{2} - 1 \approx 5.414 \)
2. \( 5 + \sqrt{3} - 1 \approx 5.732 \)