Question

show that 3/(2√5) is an irrational number ,given that √5 is irrational​

Answer 1

Let $\dfrac{3}{2\sqrt{5}}$ be a rational number.

→ $\dfrac{3}{2\sqrt{5}}=\dfrac{3}{10} \times \sqrt{5}$

Irrational/rational factors have been grouped respectively.

→ (Rational) × (Irrational) = (Rational)

→ (Rational) ÷ (Rational) = (Irrational)

Now it contradicts the definition of rational numbers. Therefore, our assumption was wrong, and therefore the given number is irrational.