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

Now, x is rational

=> x^{2} is rational

=> x^{2} - 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.