Question

The exponential form of $\sqrt{\sqrt{2}}\times \sqrt{\sqrt{3}}$

• A. $6^2$
• B. $6^{\frac{1}{2}}$
• C. $6^{\frac{1}{4}}$
• D. $6$

Answer 1

The correct option is C $6^{\frac{1}{4}}$

The given expression is $\sqrt{\sqrt{2}}\times \sqrt{\sqrt{3}}$

$={\left(\sqrt{2}\right)}^{1/2}\times {\left(\sqrt{3}\right)}^{1/2}=2^{1/2\times 1/2}\times 3^{1/2\times 1/2}=2^{1/4}\times 3^{1/4}={(2\times 3)}^{1/4}=6^{1/4}$