What is the equivalent of sqrt(2^k) and which of the following numbers is an irrational number?

The equivalent of $\sqrt{2^k}$ is:

Which of the following numbers is an irrational number?

An irrational number is a number that cannot be expressed as a simple fraction $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$. Its decimal representation is non-terminating and non-repeating.

Let's examine each option:

• A. $\frac{3}{4}$: This is a fraction of two integers, so it is a rational number.
• B. 0.333: This is a terminating decimal (or a repeating decimal if it's $0.333... = \frac{1}{3}$). Both are rational numbers.
• C. 33: This is an integer, which can be written as $\frac{33}{1}$. It is a rational number.
• D. $\sqrt{5}$: The square root of 5 is approximately 2.2360679.... This is a non-terminating and non-repeating decimal. It cannot be expressed as a simple fraction. Therefore, $\sqrt{5}$ is an irrational number.

The correct option is D.

A quarter of the volume of a cylinder with a radius of $14 \text{ mm}$ and a height of $10 \text{ cm}$? ($\pi = \frac{22}{7}$)