Question

Prove that 3√2+5 is irrational number.

Answer 1

Hello @guys
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Answer. 3√2+5 be a rational number.
.•. 3√2+5 = p/q [ where p and q are integer, q =/= 0 and q and p are co-prime number!! ]
=>3√2 = p/q-5
=>3√2 = p-5q/q
=>√2 = p-5q/3q

we know that p/q is a rational number.

.•.√2 is also a rational number.
This contradicts our assumption.
.•. 3√2+5 is an irrational number.

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Answer 2

Hey there !

Lets assume that 3√2+5 is rational.

let ,
3√2+5 = r , where "r" is rational .

3√2 = r - 5

√2 = r - 5 / 2

here ,
its very clear that , RHS is purely rational.
But on the other hand , LHS is irrational.
This is a contradiction.
Hence ,
our assumption was wrong.

therefore ,
3√2 + 5 is irrational