Question

Prove that √3+√5 is an irrational number

Answer 1

Answer: By Contradiction Method

Step-by-step explanation:

Let us assume that /2 + /5 to be a rational number

So,

We can say that :

/2 + /5 = p÷q

/2 = p÷q - /5

Hence,

As p and q are the 2 positive integers which are considered as rational numbers

So,

We can say that, the equation

p÷q -/5 is also a rational number

From this we can also conclude that /2 is also a rational number

But,

as we already know that /2 is a irrational number

So

This happened due to our wrong consumption

Hence,

By Contradiction we can say that

/2 + /5 is a irrational number

.

.

.

.

Hence proved