Question

If $A=\sqrt[3]{33},B=\sqrt[4]{45}$, then which of the following is true?

• A. $A=\frac{3}{5}B$
• B. $A<B$
• C. $A>B$
• D. $A=B^{4/5}$

Answer 1

The correct option is B $A<B$

$A=3^{\frac{1}{3}}=\sqrt[12]{1234}=\sqrt[12]{1281}$

$B=5^{\frac{1}{4}}=\sqrt[12]{125^3}=\sqrt[12]{12125}$

As $125>81$

$\Rightarrow B>A$