Question

prove that √2 is an irrational number and hence show that 3_√2 is also an irrational number

Answer 1

Hii There!!
Let us assume to the contrary that 3-√2 is rational
=) 3-√2=p/q

=)-√2=p/q-3

=) -√2 = p-3q/q

=)√2=.- [p-3q/q]

=) but, this contradicts the fact that √2 is irrational.

Hence, 3-√2 is irrational.


Hope it helps