Question

Find the order of the surd: $(\sqrt[7]{7\sqrt[3]{32}\times \sqrt{64}}{)}^{\frac{1}{10}}$

• A. $21$
• B. $20$
• C. $10$
• D. $7$

Answer 1

The correct option is A $21$

$(\sqrt[7]{7\sqrt[3]{32}\times \sqrt{64}}{)}^{\frac{1}{10}}$

$=(\sqrt[7]{72^{\frac{1}{3}}\times 2^3}{)}^{\frac{1}{10}}$

$=(\sqrt[7]{72^{\frac{10}{3}}}{)}^{\frac{1}{10}}$

$=\left(\right(2^{\frac{10}{3}}{)}^{\frac{1}{7}}{)}^{\frac{1}{10}}$

$=2^{\frac{1}{21}}$ or $\sqrt[21]{212}$

So, the order of the surd is $21$.