Question

Every surd is an irrational but every irrational need not be a surd .justify?

Answer 1

When the term surd was introduced, it was termed as another name for irrational number but today that is not the case.
Every surd is irrational but not all irrational numbers are surds. The surds in mathematics are   \pi and e and they are irrational too.
On the other hand  \sqrt{2} will give you an irrational number but this number is not called surd.

Answer 2

Answer:

By definition , a surd is an irrational root of a rational number.So now we know that surds are always irrational and they are always roots.

For example , square root of 2 is a surd since 2 is rational and square root of 2 is irrational

similarly, cube root of 9 is also a surd since 9 is rational and cube root of 9 is irrational.

On the other hand, is not a surd even though is irrational, because is not rational.