Question

given that under root 2 is irrational prove that 5 +3 under root 2 is an irrational number

Answer 1

Let us assume that 5+3 under root 2 is rational
5+3under root 2=p/q,where p and q are coprimes and q not equals to 0 .
3 under root 2=p/q-5
under root 2=p/q-5/3.
Here, a rational number never equals to an irrational number.
but we assume that p and q are coprimes and q not equals to 0.
Our assumption is wrong.
so, 5+3under root 2 is irrational.
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