Question

Comment on the statement:
All surds are irrational numbers, but all irrational numbers are not surds.

• A. The statement is correct.
• B. The statement is wrong.
• C. Cannot be determined.

Answer 1

The correct option is A The statement is correct.

Surd is $n^{th}$ root of a positive integer which can be simplified into a rational number.

Let's take an example.

$\sqrt{5}$ is a surd. It cannot be expressed as $\frac{p}{q}$ form, given that $p$ and $q$ are integers and $q\ne 0.$

$\pi$ is an irrational number, but it is not a surd as it cannot be expressed as $n^{th}$ root of a positive integer i.e. $\sqrt[n]{na}.$

$\therefore$ All surds are irrational numbers, but vice versa is not valid.