Question

show that 2 + root 3 is an irrational​

Answer 1

2+√3 is an irrational number because √3 is not a perfect square

it is non terminating non reccuring

so it is a irrational number

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Answer 2

assume that 2+√3 is a rational

2+√3=a/b(we say)(where a&b are co-primes)

√3=a/b-2

√3=(a-2b)/b

hear, RHS is rational . then, LHS is also rational.this is contradiction.because,√3 is a irrational.

then, we say 2+√3 is irrational.