prove that root 5-3 root 2 is an irrational number

*to prove that 5-3√2 is an irrational number:*

*Assume that 5-3√2 is a rational number*

*i.e. 5-3 √2 = p/q (p and q are integers, q*

*≠0 , p and q are co-primes)*

*Now take all the rational no. from R.H.S and L.H.S to 1 side*

*5/1-p/q = 3√2*

*5q-p/q = 3√2 (i.e 3*√2)*

*5q/3 – p/3q = √2*

*Since p and q are integers (rational no.) ,5q/3 – p/3q should also be a rational no.*

*But √2 is irrational*

*Which contradicts our assumption is wrong*

*Therefore 5-3√2 is an irrational no.*
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