Question

which numbers are irrational numbers?
select each correct answer.
$pi$
$sqrt{\frac{10}{49}}$
0.5
3.14

Explanation:

Step1: Define irrational numbers

Irrational numbers are non-repeating, non-terminating decimals that cannot be written as a ratio of two integers.

Step2: Analyze $\pi$

$\pi$ has a non-repeating, non-terminating decimal expansion and cannot be expressed as $\frac{a}{b}$ (where $a,b$ are integers, $b
eq0$). So it is irrational.

Step3: Simplify $\sqrt{\frac{10}{49}}$

$\sqrt{\frac{10}{49}}=\frac{\sqrt{10}}{7}$. $\sqrt{10}$ is irrational, so $\frac{\sqrt{10}}{7}$ is irrational.

Step4: Analyze 0.5

$0.5=\frac{1}{2}$, a ratio of integers. It is rational.

Step5: Analyze 3.14

$3.14=\frac{314}{100}=\frac{157}{50}$, a ratio of integers. It is rational.

Answer:

$\pi$, $\sqrt{\frac{10}{49}}$