Question

Write $\sqrt[4]{46},\sqrt{2},\sqrt[3]{34}$ in ascending order

• A. $\sqrt{2},\sqrt[4]{46}$ and $\sqrt[3]{34}$
• B. $\sqrt[4]{46}$, $\sqrt{2}$ and $\sqrt[3]{34}$
• C. $\sqrt{2}$, $\sqrt[3]{34}$ and $\sqrt[4]{46}$
  
• D. None of these

Answer 1

Answer: (A)

$\sqrt{2},\sqrt[4]{46}$ and $\sqrt[3]{34}$

$6^{\frac{1}{4}},2^{\frac{1}{2}},4^{\frac{1}{3}}$
The surds are of the order $4,2$ and $3$ respectively The L.C.M. is $12$ So, we change each surd of the order $12$
The terms now are ${\left(6^3\right)}^{\frac{1}{12}},{\left(2^6\right)}^{\frac{1}{12}}$ and ${\left(4^4\right)}^{\frac{1}{12}}$
$\Rightarrow {\left(216\right)}^{\frac{1}{12}},{\left(64\right)}^{\frac{1}{12}}$ and ${\left(256\right)}^{\frac{1}{12}}$
$\therefore$ Ascending order is $\sqrt{2},\sqrt[4]{46}$ and $\sqrt[3]{34}$