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4. Insert two irrational numbers between 2 and 2.5.

5. Write three irrational numbers between 0.5 and 0.6.

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Certainly! Let's solve the given problems step by step.

### 4. Insert two irrational numbers between 2 and 2.5

We need to find two irrational numbers that fall between 2 and 2.5. Through careful consideration, the two irrational numbers can be:

- First irrational number: 2.1414213562373097
- Second irrational number: 2.1858407346410207

Thus, the two irrational numbers between 2 and 2.5 are:
[tex]\[ 2.1414213562373097 \][/tex]
[tex]\[ 2.1858407346410207 \][/tex]

### 5. Write three irrational numbers between 0.5 and 0.6

We need to find three irrational numbers that lie within the interval 0.5 to 0.6. Through thorough analysis, three such numbers are:

- First irrational number: 0.6118033988749895
- Second irrational number: 0.6495996501709426
- Third irrational number: 0.6235582649299566

Thus, the three irrational numbers between 0.5 and 0.6 are:
[tex]\[ 0.6118033988749895 \][/tex]
[tex]\[ 0.6495996501709426 \][/tex]
[tex]\[ 0.6235582649299566 \][/tex]

To recap:
- Two irrational numbers between 2 and 2.5 are [tex]\( 2.1414213562373097 \)[/tex] and [tex]\( 2.1858407346410207 \)[/tex].
- Three irrational numbers between 0.5 and 0.6 are [tex]\( 0.6118033988749895 \)[/tex], [tex]\( 0.6495996501709426 \)[/tex], and [tex]\( 0.6235582649299566 \)[/tex].

This completes our solution for the given questions.
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