Question

prove 5+3√2 is a irrational number​

Answer 1

when we add, subtract, multiply or divide rational no. with any irrational no. we get irrational no.

root 2 is irrational

when we multiply 3 by root 2 we will get irrational no.

and when we add 5 to irrational no. we will get irrational no.

Therefore it is irrational no.

Answer 2

Assume to reach our contradiction that 5 + 3√2 is a rational number.

Let x = 5 + 3√2, where x is a rational number which values the RHS.

  ⇒ x = 5 + 3√2

  ⇒ x - 5 = 3√2

  ⇒ (x - 5)/3 = √2

Here it creates a contradiction that the LHS of (x - 5)/3 = √2 is rational while the RHS is irrational.

Hence proved that 5 + 3√2 is irrational.