Answer :

If possible, let be a rational number equal to x. Then,

= (√3)^{2} + (√5)^{2} + 2 × √3 × √5

= 3 + 5 + 2√15

= 8 + 2√15

x^{2} – 8 = 2√15

Now, x is rational

x^{2} is rational.

is rational.

√15 is rational.

But, √15 is irrational

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

Hence, + is an irrational number.

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