Question

1. which set(s) of numbers does $sqrt{20}$ belong to? choose all that apply.$square$ natural numbers$square$ whole numbers$square$ integers$square$ rational numbers$square$ irrational numbers

Explanation:

Step1: Simplify the square root

$\sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}$

Step2: Classify the number

$\sqrt{5}$ is non-terminating, non-repeating, so $2\sqrt{5}$ cannot be written as $\frac{a}{b}$ where $a,b$ are integers ($b
eq0$). Thus it is irrational, and all irrational numbers are real numbers.

Step3: Eliminate other sets

Natural, whole, integer, and rational numbers require the number to be a terminating/repeating decimal or integer, which $\sqrt{20}$ is not.

Answer:

Irrational Numbers