Question

prove that 3 minus 2 root 5 is an irrational number

Answer 1

3-2√5 is an irrational number.

→If possible let us assume that 3-2√5 is rational.
→So it can be written in form p/q where p and q are coprimes and q≠0

3-2√5=p/q
3-p/q=2√5
(3q-p)/q=2√5

$\frac{3q - p}{2q} = \sqrt{5}$
As p/q is rational so (3q-p)/2q is also rational but √5 is irrational. This contratiction has arised due to oyr wrong assumption.

so 3-2√5 is also irrrational

Answer 2

Answer:

so, this is your answer .