Question

classify the numbers as rational or irrational.
2
$sqrt{40}$
$2 cdot sqrt{40}$
rational
irrational

Explanation:

Step1: Identify rationality of 2

A rational number can be written as $\frac{p}{q}$ where $p,q$ are integers, $q
eq0$. $2 = \frac{2}{1}$, so it is rational.

Step2: Simplify $\sqrt{40}$

$\sqrt{40} = \sqrt{4\times10} = 2\sqrt{10}$. $\sqrt{10}$ is non-terminating, non-repeating, so $\sqrt{40}$ is irrational.

Step3: Analyze $2\cdot\sqrt{40}$

$2\cdot\sqrt{40}=2\times2\sqrt{10}=4\sqrt{10}$. Since $\sqrt{10}$ is irrational, multiplying by integer 4 keeps it irrational.

Answer:

rational: $2$
irrational: $\sqrt{40}$, $2\cdot\sqrt{40}$