Question

prove that 2/✓3+3 is irrational

Answer 1

☆Let us assume that 2/root3 +3 is rational number.

2/root 3=p/q.

☆Reciprocal numerator and denominator of both sides.

root 3+3/2=q/p.

root3+3=2q/p.

root 3=2q/p-3.

root3=2q-3p/p.

☆Here root 3 is irrational.

☆Irrational is not equal to rational.

☆LHS is not equal to RHS.

☆This contradicts to our assumption.

☆Thus we can say that 2/root3+3 is irrational number.

Hope it helps u.☆☆