Question

The biggest among the following is

• A. $2^{1/2}$
• B. $3^{1/3}$
• C. $6^{1/6}$
• D. $8^{1/8}$

Answer 1

The correct option is B $3^{1/3}$

L.C.M of $2,3,6,8=24$
$2^{\frac{1}{2}}=2^{\frac{12}{24}}$
$3^{\frac{1}{3}}=3^{\frac{8}{24}}$
$6^{\frac{1}{6}}=6^{\frac{4}{24}}$
$8^{\frac{1}{8}}=8^{\frac{3}{24}}$
$\therefore 8^3<6^4<2^{12}<3^3$
$=>8^{\frac{3}{24}}<6^{\frac{4}{24}}<2^{\frac{12}{24}}<3^{\frac{8}{12}}$
$=>8^{\frac{1}{8}}<6^{\frac{1}{6}}<2^{\frac{1}{2}}<3^{\frac{1}{3}}$