Question

Prove that √5-3√2 is an irrational number

Answer 1

$\huge\underline{\underline{\maltese\: \: \textbf{\textsf{Answer}}}}$

In √5−3√2,

the number √2 is an irrational number.

Also, 5 is a rational number.

We know, the difference of a rational number and an irrational number is always an irrational number.

Therefore, since √2 is an irrational number, √5−3√2 is also an irrational number.

$\sf\red{\fbox{\tt{∴ Hence proved.}}}$