Question

For the following statement choose the correct option.

$\sqrt[4]{412}\times \sqrt[7]{76}$ is equal to $168\sqrt{2}.$

• A. The given statement is true.
• B. The given statement is false.
• C. Incomplete information
• D. None of the above

Answer 1

The correct option is B The given statement is false.

$\sqrt[4]{412}\times \sqrt[7]{76}$

$={\left(12\right)}^{\frac{1}{4}}\times {\left(6\right)}^{\frac{1}{7}}$

$=2^{\frac{1}{4}}\times 6^{\frac{1}{4}}\times 6^{\frac{1}{7}}$

$=2^{\frac{1}{4}}\times 6^{(\frac{1}{4}+\frac{1}{7})}$

$=2^{\frac{1}{4}}\times 6^{\frac{11}{28}}$

The given statement is false.