Question

Q-11.Prove that 3 + 2√3 is an irrational number.
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Answer 1

Answer:

3÷2√3 =3√3/6 =(√3)/2, and if it equals a rational number m/n, then multiplying by √3, we get that √3 = 2.m/n which is again rational. But we know that if a square root of a positive integer k is rational, then k must be a perfect square. As 3 is not a perfect square, we see that √3 is irrational. This shows that (3÷2√3) is irrational.