Question

$\sqrt[4]{} \sqrt[3]{2 {}^{2} }$
​

Answer 1

Answer:

$\sqrt[4]{} \sqrt[3]{2 {}^{2} }$

= $\sqrt[4]{} \sqrt[3]{4}$

= 1.1

✔

Answer 2

$\huge{\balck{\boxed{ \sqrt[4]{} \sqrt[3]{2 {}^{2} } = \sqrt[4]{} \sqrt[3]{4}}}}}}}}}}}}}}}}$

$\large\boxed{\fcolorbox{First}{\:Let\:us\:solve\:for\:\sqrt[3]{4}}}$

∛4 = 1.587

$\large\boxed{\fcolorbox{Now}{\:Let\:us\:solve\:for\:\sqrt[4]{1.587}}}$

TO SOLVE THIS WE SHOULD KNOW ABOUT De Moivre's Theorem

$\large{\green{\boxed{\sqrt[n]{1} = cos\dfrac{2k\pi}{n} + sin\dfrac{2k\pi}{n} \, i}}}}}}}}}}}}}}}$

$\large{\green{\boxed{\sqrt[n]{-1} = cos\dfrac{(2k+1)\pi}{n} + sin\dfrac{(2k+1)\pi}{n} \, i}}}}}}}}}}}}}}}$

$\huge\boxed{\sqrt[4]{1.587} = 1.12239115}}}$