Question

given that√2is irrational prove that(5+3√2)an irrational number

Answer 1

5 is a rational number.
3is also a rational number

√2 is a iretional number.

3√2 is a irrational number as... product of rational and irrational is always irrational..

also, 5+3√2 is a irrational number as.. sum of irrational.and rational number is also irrational..


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Answer 2

hey..
here's ur solution,

let,
us assume contrary that 5 + 3 root 2 is rational.

let
5+ 3 root 2 = a/b.....( where a and b are co -Prime )

hence LHS is rational.

but we know that root 2 is irrational.
it is not possible,

so our supposition is wrong.

5 + 3 root 2 is not rational.

hence it is irrational.