Question

Which of the following has the same value as the expression $\sqrt{2}\times \sqrt[4]{42}$

• A. $\sqrt[4]{48}$
• B. $\sqrt[6]{62}$
• C. $\sqrt[8]{82}$
• D. $\sqrt[8]{84}$

Answer 1

The correct option is A $\sqrt[4]{48}$

The value of the expression $\sqrt{2}\times \sqrt[4]{42}$

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

$=$ $2^{\frac{1}{2}+\frac{1}{4}}$ .... By law $a^m\times a^n=a^{m+n}$

$=$ $2^{\frac{3}{4}}$

$=$ $\sqrt[4]{48}$