Question

prove that (3+2√5)2 is irrational​

Answer 1

to prove - (3+2✓5)2 is irrational no.

proved - let (3+2✓5)2 = M

so, (3+2✓5) = M/2

=} 2✓5 = M/2 - 3

then

✓5 = (M/2 - 3)/2

We know that ✓5 is irrational no.

so (M/2 - 3)/2 is also irrational no.

then, M is also irrational no. so (3+2✓5)2 is also irrational no.

-----proof------