Q. 113.8( 85 Votes )

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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


x2 – 8 = 2√15



Now, x is rational


x2 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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