Let x and y be rational and irrational numbers respectively. Is x + y necessarily an irrational number? Give an example in support

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   Let x and y be rational and irrational numbers , respectively. Is x+y necessarily an irrational number

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   Yes ,(x+y) is necessarily an irrational number . <br> e.g… Let

   <br> Then,

   <br> if possible, let x+y =2

   be a rational number. <br> Consider ,

   <br> On Squaring both sides, we get <br>

   <br>

   <br>

   <br> So, a is rational

   is rational

   is rational. <br> But, this contradicits the fact that

   is an irrational number. thus, our assumption is wrong. <br> Hence, x+ y is an irraional number.

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