Question

Is the number $\sqrt[4]{416}$ a surd?

• A. yes
• B. no

Answer 1

The correct option is B no

For the number $\sqrt[4]{416}$ to be a surd, it should not be a rational number after simplification.

Simplifying $\sqrt[4]{416}$
$\sqrt[4]{416}=\sqrt[4]{42^4}$
$=(2^4{)}^{1/4}=2^{4\times \frac{1}{4}}$
$=2^1=2$

As $2$ is a rational number, hence $\sqrt[4]{416}$ is not a surd.