Question

Which of the following numbers are irrational numbers?

• A. $2-\sqrt{5}$
• B. $\left(3+\sqrt{23}\right)-\left(\sqrt{23}\right)$
• C. $\frac{1}{\sqrt{2}}$
• D. $2\pi$

Answer 1

Answer: (A), (C), (D)

The correct options are
A $2-\sqrt{5}$
C $\frac{1}{\sqrt{2}}$
D $2\pi$

$A$ is a irrational number as it cannot be expressed of the form $\frac{p}{q}$

$B$ is a rational number. As it can be expressed in the form of $\frac{3}{1}$

$C$ is a irrational number as it cannot be expressed of the form $\frac{p}{q}$

$D$ is a irrational number as $\pi$ is itself irrational and the product of irrational with rational is always irrational.