Question

mark the subsets each number belongs to in the chart. natural whole integer rational irrational real $sqrt{256}$ 0 $pi$

Explanation:

Step1: Evaluate $\sqrt{256}$

$\sqrt{256}=16$. Natural numbers are positive integers starting from 1, so 16 is a natural number. Whole numbers include 0 and natural numbers, so 16 is a whole number. Integers include positive and negative whole - numbers and 0, so 16 is an integer. Rational numbers are numbers that can be written as a fraction $\frac{a}{b}$ where $b
eq0$, and 16 can be written as $\frac{16}{1}$, so it is rational. Since it is rational, it is not irrational. All rational numbers are real numbers, so it is real.

Step2: Analyze 0

0 is not a natural number (natural numbers start from 1). 0 is a whole number. 0 is an integer. 0 can be written as $\frac{0}{1}$, so it is rational. Since it is rational, it is not irrational. 0 is a real number.

Step3: Analyze $\pi$

$\pi$ is not a natural number. $\pi$ is not a whole number. $\pi$ is not an integer. $\pi$ cannot be written as a fraction $\frac{a}{b}$ where $a,b\in\mathbb{Z}$ and $b
eq0$, so it is irrational. Since irrational numbers are part of the real - number set, $\pi$ is real.

Answer:

Number	Natural	Whole	Integer	Rational	Irrational	Real
0		$\boxed{\surd}$	$\boxed{\surd}$	$\boxed{\surd}$		$\boxed{\surd}$
$\pi$					$\boxed{\surd}$	$\boxed{\surd}$