Question

The simplest rationalising factor of $\sqrt[4]{448}$ is

• A. $\sqrt[4]{49}$
• B. $\sqrt[4]{427}$
• C. $\sqrt[3]{39}$
• D. none of these

Answer 1

The correct option is B $\sqrt[4]{427}$

Given that,$\sqrt[4]{448}$

Now,$\sqrt[4]{448}=\sqrt[4]{42^4\times 3}=2\sqrt[4]{43}$

So,

$2\sqrt[4]{43}=\frac{2\sqrt[4]{43}\times \sqrt[4]{43^3}}{\sqrt[4]{43^3}}=\frac{2\sqrt[4]{43^4}}{\sqrt[4]{427}}=\frac{2\times 3}{\sqrt[4]{427}}=\frac{6}{\sqrt[4]{427}}$

We get a rational number by multiplying $\sqrt[4]{427}$ with $\sqrt[4]{448}$

Hence, rationalising factor of $\sqrt[4]{448}$ is $\sqrt[4]{427}$.

Hence, option B is the answer.