Question

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

Answer 1

Answer:

let suppose √2-3√5 is a rational no.

then we can write it as

√2-3√5=p/q

q not equal to 0

p and q are co prime integers

√2 = p/q + 3√5

√2 = p+ 3√5/q

here we see that p+3√5/q are all integers

so p+3√5 is rational

so we say that √2 is also rational

but we know that √2 is an irrational number

so there is a contradiction

our assumption is wrong

hence √2-3√5 is irrational number