Question

Identify wheather $\sqrt[4]{481\times 49}$ is a surd.

• A. It is a surd. Its simplified value is $7\sqrt{3}.$
• B. It is a surd. Its simplified value is $3\sqrt{7}.$
• C. It is not a surd.

Answer 1

The correct option is B It is a surd. Its simplified value is $3\sqrt{7}.$

Let's simplify $\sqrt[4]{481\times 49}$ by factorization.

$\sqrt[4]{481\times 49}=\sqrt[4]{4(3\times 3\times 3\times 3)\times (7\times 7)}=3\sqrt[4]{47\times 7}=3\times (7^2{)}^{\frac{1}{4}}=3\times (7{)}^{\frac{1}{2}}$
$=3\sqrt{7}$

$3\sqrt{7}$ is a surd because it can not be simplified into a rational number.