Question

Which among the following numbers is the greatest?
$\sqrt[3]{34},\sqrt{2},\sqrt[6]{613},\sqrt[4]{45}$

• A. $\sqrt[3]{34}$ is the greatest
• B. $\sqrt{2}$ is the greatest
• C. $\sqrt[6]{613}$ is the greatest
• D. $\sqrt[4]{45}$ is the greatest

Answer 1

The correct option is A $\sqrt[3]{34}$ is the greatest

LCM of $3,6,4=12$

So, raising each given number to power $12$.
$\Rightarrow \sqrt[3]{34}=(4{)}^{1/3}=(4^{1/3}{)}^{12}=4^4=256$
$\Rightarrow \sqrt{2}=(2{)}^{1/2}=(2^{1/2}{)}^{12}=2^6=64$
$\Rightarrow \sqrt[6]{613}=(13{)}^{1/6}=({13}^{1/6}{)}^{12}={13}^2=169$
$\Rightarrow \sqrt[4]{45}=(5{)}^{1/4}=({15}^{1/4}{)}^{12}=5^3=125$

$\therefore \sqrt[3]{34}$ is the greatest.