Question

Which is the greatest among √2, ³√4and ⁴√3
step by step explaination​

Answer 1

Answer:

Taking LCM of 2,3  and 4

we get it is 12

so,

$\sqrt{2}$ = $\sqrt[12]{2^{6} }$ =$\sqrt[12]{64}$

$\sqrt[3]{4}$ = $\sqrt[12]{4^{4} }$ =$\sqrt[12]{256}$

$\sqrt[4]{3}$ = $\sqrt[12]{3^{3} }$ = $\sqrt[12]{27}$

As we get figuring in those three surds,

27<64<256

Hence,  $\sqrt[3]{4}$ is the greatest among them.