Question

Prove that 3+5√2 is an irrational number​

Answer 1

Answer:

Let us assume, to the contrary , that 3+5√2 is a rational number.

Now , let 3+5√2 =a/b , where a and b are coprimes and b≠0.

So, 5√2=a/b - 3 or √2=a/5b - 3/5

Since a and b are integers , therefore

a/5b - 3/5 is a rational number

.: √2 is rational number.

But √2 is an irrational number.

This shows that our assumption is incorrect.

So, 3+5√2 is an irrational number.

Hence, proved.