The image you uploaded contains a question asking you to classify various number sets based on whether the numbers are rational or irrational.

Here are the sets:

a) $\left(\sqrt{25}, \sqrt{9}, \sqrt{64}\right)$

• All of these are perfect squares: $\sqrt{25} = 5$, $\sqrt{9} = 3$, and $\sqrt{64} = 8$. These are all rational numbers because they can be expressed as simple fractions (e.g., 5/1, 3/1, 8/1).
• The correct description: Only Rational Numbers

b) $(-2.4, 0, 3.1, \sqrt{81})$

• $-2.4$ is a decimal, and decimals that terminate or repeat are rational.
• $0$ is an integer, so it's rational.
• $3.1$ is also a decimal and is rational.
• $\sqrt{81} = 9$, which is a rational number.
• The correct description: Both Rational & Irrational Numbers (since these are all rational numbers).

c) $\left(-\frac{2}{3}, \frac{7}{9}, \frac{\pi}{2}\right)$

• $-\frac{2}{3}$ and $\frac{7}{9}$ are both rational numbers, as they can be written as fractions.
• $\frac{\pi}{2}$ involves the irrational number $\pi$, and dividing an irrational number by a rational number results in an irrational number.
• The correct description: Both Rational & Irrational Numbers

d) $\left(\sqrt{12}, \sqrt{11}, \pi\right)$

• $\sqrt{12}$ and $\sqrt{11}$ are irrational numbers (they cannot be simplified into rational numbers).
• $\pi$ is an irrational number.
• The correct description: Only Irrational Numbers

Would you like me to provide further details or help with any other questions?

Here are some related questions:

1. How do you identify rational and irrational numbers?
2. What makes a number rational or irrational?
3. What is the difference between a terminating decimal and a repeating decimal?
4. How can you simplify square roots to determine whether a number is rational?
5. What are some common irrational numbers besides $\pi$ and $\sqrt{2}$?

Tip: Remember that any number that can be expressed as a fraction of two integers is rational, while numbers that cannot, like square roots of non-perfect squares or transcendental numbers like $\pi$, are irrational.