Question

given that root 2 is irrational proof then 5 + 3 root 2 is an irrational number

Answer 1

hey frnd..

ur solution is here...

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Answer 2

let us assume that 5 + 3√2 is a rational number.
Then there exist a co-prime positive integers p and q such that
5+3√2 = p÷q
3√2 = p÷q -5
3√2= p-5q÷q
√2 = p-5q ÷3q (p,q are inteaser. So, p-5q÷3q is rational)
Hence, √2 is rational
But it contradict the fact that √2 is irrational
This contradiction arises because our assumption is wrong
5+3√2 is irrational number