Question

Every surd is an irrational, but every irrational need not be a surd. Justify your answer.

Answer 1

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 $2$ i.e. $\sqrt{2}$ 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, $\pi$ and $e$ are not surds even though they are irrational, because they are not the roots of any algebraic expression.