Question

Which of the following is a surd?

• A. $\sqrt[5]{5100000}$
• B. $\sqrt[4]{481}$
• C. $\sqrt[343]{3433}$
• D. $\sqrt[3]{3343}$

Answer 1

The correct option is C $\sqrt[343]{3433}$

We know that Surd is $n^{th}$ root of a positive number which can not be simplified into a rational number.

$\sqrt[5]{5100000}=({10}^5{)}^{\frac{1}{5}}=10$
Hence, it is not a surd.

$\sqrt[4]{481}=(3^4{)}^{\frac{1}{4}}=3$
Hence, it is not a surd.

$\sqrt[343]{3433}=(3{)}^{\frac{1}{343}}$
Hence, it is a surd.

$\sqrt[3]{3343}=(7^3{)}^{\frac{1}{3}}=7$
Hence, it is not a surd.