Question

please answer my above questions it is of the real numbers proving questions.

Answer 1

Heya !!

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Given that √2 is irrational.

Let 5+3√2 be rational.

5+3√2 = a/b where a and b are integers and (b≠0)

=> 3√2 = (a/b) – 5

=> √2 = (a–5b) / 3b

Since √2 is irrational.
Thus, (a–5b) /3b is also irrational.

But this contradiction has arisen because of our incorrect consumption.

So, we conclude that 5+3√2 is an irrational number.

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Hope my ans.'s satisfactory.☺

Answer 2

Root 2 is irrational. Or 5 and 3 is rational. The sum of rational and irrational is always irrational. Hence proved.