Question

Show that 3√5 is an irrational number

Answer 1

We have to prove that 3√5 is an irrational number.

let us assume 3√5 is a rational number where a , b are some integers.

thus,  

3√5 = a/b

√5 = a/b × 1/3

√5 = a/3b

Here,

In RHS, 3 , a , b are rational integers.

⇒ LHS is also rational .i.e: √5 is rational number

Thus, this contradicts the fact that √5 is irrational number.

So, this contradiction arise due to our wrong assumption.

Thus, 3√5 is an irrational number.

Hence,proved.