Question

Given that under root 2 is irrational, prove that (5+3 under root 2) is an irrational.

Answer 1

hi

This question came in maths exam

solution

⭐Let 5+ 3√2 be rational number say p/q

5+ 3√2 = p/q

√2=p/q - 5

√2=p-5q/3q

$\frac{p - 5q}{3q} \: is \: ratinonal \: so \sqrt{2} should \: be \\ also \: rational \:$
⭐But it is given that √2 is irrational

⭐There is contradiction so our assumption is wrong

⭐Given number is irrational



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