To find three irrational numbers between $\frac{1}{4}$ (0.25) and $\frac{4}{5}$ (0.8), we need numbers within this range that cannot be expressed as a ratio of integers (irrational numbers). Examples include non-repeating, non-terminating decimals or roots of non-perfect squares.

Here are three irrational numbers within this range:

1. $\sqrt{0.3} \approx 0.5477$
2. $\pi / 4 \approx 0.7854$
3. $\sqrt{2} - 1 \approx 0.4142$

These are irrational because:

• $\sqrt{0.3}$ involves the square root of a non-perfect square.
• $\pi / 4$ is derived from $\pi$, which is a well-known irrational number.
• $\sqrt{2} - 1$ involves the subtraction of a rational number from an irrational one, maintaining irrationality.

Would you like a more detailed explanation about irrational numbers or this specific range?

Related Questions

1. What are some other irrational numbers between $\frac{1}{4}$ and $\frac{4}{5}$?
2. Can irrational numbers be used in algebraic equations? Provide examples.
3. How can we prove that $\sqrt{0.3}$ is irrational?
4. What is the difference between rational and irrational numbers?
5. Why is $\pi$ considered irrational?

Tip

Always check if a square root or fractional value simplifies to a rational number when seeking examples of irrational numbers.