Question

Consider the given statements:
I. All surds are irrational numbers.
II. All irrationals numbers are surds.
Which of the following is true.

• A. Only I
• B. Only II
• C. Both I and II
• D. Neither I nor II

Answer 1

The correct option is A Only I

A surd, by its very definition, is an irrational root of a rational number, i.e. it is an irrational number.

Eg.: $\sqrt{2}$ is a surd as $2$ is a rational and $\sqrt{2}$ is irrational.

However, not every irrational number can be expressed as a surd.

Eg.: $\pi$ is not a surd even though it is an irrational number.

Hence, only statement $1$ is true.

Therefore, option $A$ is correct.