Prove the following number is Irrational/Not Rational: 5+3?2

5 + 3 √2 is an irrational number is to be proved.

Let 5 + 3 √2 is a rational number

So p/q = 5 + 3 √2

p = 5q + 3q√2

p – 5q = 3q√2

p – 5q / 3q = √2

p/2q – 5q/3q = √2

p/3q = 5/3 = √2

Here 5/3 is a rational number. Both terms are rational and therefore 5 + 3 √2 is an irrational number

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