Let's solve the questions one by one from the image.

2. a) Write down any rational number between 4 and 6.

A rational number is any number that can be expressed as the ratio of two integers (like fractions or whole numbers).

• An example of a rational number between 4 and 6 is 5 or 4.5.

2. b) Write down any irrational number between 4 and 6.

An irrational number is a number that cannot be expressed as a ratio of two integers. Its decimal expansion goes on forever without repeating.

• An example of an irrational number between 4 and 6 is √18, since √18 ≈ 4.24 and is irrational.

2. c) Find a rational number between √2 and √3.

We need to find a rational number between the approximations of √2 and √3.

• √2 ≈ 1.414, and √3 ≈ 1.732. A rational number between them could be 1.5 or 1.6.

2. d) Write down any rational number between π and √10.

We need a rational number between π ≈ 3.1416 and √10 ≈ 3.1623.

• A rational number between them could be 3.15.

Do you want any further explanation on these problems?

Related Questions:

1. What is the difference between rational and irrational numbers?
2. How do you approximate irrational numbers like √2 and √3?
3. Can every number between two irrational numbers be rational?
4. What are some methods for finding rational approximations of π?
5. Why can't irrational numbers be expressed as fractions?

Tip: When approximating irrational numbers, it's useful to know a few key square roots like √2 ≈ 1.414 and √3 ≈ 1.732 to help find rational numbers between them.