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Prove that √3 + √5 is an irrational number

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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.

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