Answer :

Let us suppose that √3 + √5 is rational. Let √3 = √5 − a, were a is rational.

On squaring both sides, we get

(√3)^{2} = (√5 – a )^{2}

**⇒** 3 = 5 + a^{2} − 2a√5 [ Using (a-b)^{2} = a^{2} + b^{2} + 2ab]

**⇒** 2a√5 = 2 + a^{2}

This is not possible because right hand side is rational while left hand side i.e. √5 is irrational.

So, our assumption is wrong. **√3 + √5 is irrational.**

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