Question

State whether the statement is true or false.
All surds are irrational but not all rational numbers are surds.

• A. True
• B. False

Answer 1

The correct option is B False

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

For eg, √2 is a surd since 2 is rational and √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, √π is not a surd even though √π is irrational because π is not rational.
Therefore, every surd is an irrational number but an irrational number may or may not be a surd.