Question

State with reason, whether the following is a surd.

`sqrt(3 + sqrt(5))`

Answer 1

`sqrt(3 + sqrt(5))` is a surd

Reason:

• A surd is an irrational root that cannot be simplified to remove the root sign and become a rational number.
• Inside the outer square root, the term `(3 + sqrt(5))` itself includes `(sqrt(5))` which is irrational.
• The entire expression `(sqrt(3 + sqrt(5)))` cannot be simplified to a rational number.
• Therefore, `(sqrt(3 + sqrt(5)))` is irrational and hence a surd.