Questions: Which of the following are irrational numbers? Select all correct answers. Select all that apply: √18 0.4848848884 ... √17

Solution Steps

To determine which numbers are irrational, we need to understand the definition of an irrational number. An irrational number cannot be expressed as a simple fraction, and its decimal representation is non-repeating and non-terminating.

1. $\sqrt{18}$:

   • The square root of 18 is not a perfect square, and its decimal representation is non-repeating and non-terminating. Therefore, $\sqrt{18}$ is an irrational number.

2. $0.4848848884 \ldots$:

   • This number has a repeating pattern in its decimal representation (4848848884...), which means it is a rational number.

3. 5:

   • The number 5 is an integer and can be expressed as a fraction (5/1), so it is a rational number.

4. $\sqrt{17}$:

   • The square root of 17 is not a perfect square, and its decimal representation is non-repeating and non-terminating. Therefore, $\sqrt{17}$ is an irrational number.

5. 2.65:

   • This is a terminating decimal and can be expressed as a fraction (265/100), so it is a rational number.

6. $\frac{25}{22}$:

   • This is a fraction, which means it is a rational number.

Final Answer