Check whether $7 \sqrt{5}$,$\frac{7}{\sqrt{5}}$,$\sqrt{2}+21$,and $\pi-2$ are irrational numbers or not.

(N/A) To determine if a number is irrational,we check if it can be expressed as a non-terminating,non-recurring decimal.
$1$. $7 \sqrt{5}$: Since $\sqrt{5} \approx 2.236$ is an irrational number,the product of a non-zero rational number $(7)$ and an irrational number $(\sqrt{5})$ is always irrational. Thus,$7 \sqrt{5} \approx 15.652...$ is irrational.
$2$. $\frac{7}{\sqrt{5}}$: Rationalizing the denominator,we get $\frac{7 \sqrt{5}}{5} \approx 3.1304...$. Since the quotient of a non-zero rational number and an irrational number is irrational,$\frac{7}{\sqrt{5}}$ is irrational.
$3$. $\sqrt{2}+21$: Since $\sqrt{2} \approx 1.414$ is irrational,the sum of an irrational number and a rational number $(21)$ is always irrational. Thus,$\sqrt{2}+21 \approx 22.414...$ is irrational.
$4$. $\pi-2$: Since $\pi \approx 3.1415...$ is an irrational number,the difference between an irrational number and a rational number $(2)$ is always irrational. Thus,$\pi-2 \approx 1.1415...$ is irrational.
Conclusion: All the given numbers are irrational.