Question

which of the following is an irrational number?
○ $\sqrt{4}$
○ $\sqrt{9}$
○ $\sqrt{16}$
○ $\sqrt{20}$

Explanation:

Step1: Simplify $\sqrt{4}$

$\sqrt{4} = 2$, which is rational.

Step2: Simplify $\sqrt{9}$

$\sqrt{9} = 3$, which is rational.

Step3: Simplify $\sqrt{16}$

$\sqrt{16} = 4$, which is rational.

Step4: Simplify $\sqrt{20}$

$\sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}$. $\sqrt{5}$ is irrational, so $2\sqrt{5}$ is irrational.

Answer:

$\boldsymbol{\sqrt{20}}$ (the last option)