Question

Prove that √3 + √5 is an irrational number

Answer 1

If possible, let √3 + √5 be a rational number equal to x. Then,

Now, x is rational 

=> x² is rational 

=> x² - 8/2 is rational

=> √15 is rational

 But, √15 is rational 

Thus, we arrive at a contradiction. So, our supposition that √3 +√5  is rational is wrong. 

Hence, √3 + √5  is an irrational number.