Question

simplify 4 under root 3 under root 2 square

Answer 1

Answer:

$\sqrt[4]{\sqrt[3]{2^2}}=2^{\frac{1}{6}}$

Step-by-step explanation:

Concept used:

$\sqrt[n]{a}=a^{\frac{1}{n}}$

$(a^m)^n=a^{mn}$

Given:

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

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

$=\sqrt[4]{4^{\frac{1}{3}}}$

$=({4^{\frac{1}{3}}})^{\frac{1}{4}}$

$=4^({\frac{1}{3}.\frac{1}{4}})$

$=4^{\frac{1}{3.4}}$

$=4^{\frac{1}{12}}$

$=(2^2)^{\frac{1}{12}}$

$=2^{\frac{2}{12}}$

$=2^{\frac{1}{6}}$

Answer 2

Answer:

The correct answer is $=2^{1/6}$

Step-by-step explanation:

The given question is $\sqrt[4]{\sqrt[3]{2^{2}}}$

Formula used: $\sqrt[n]{a}=a^{1/n}$

$(a^{m})^{n}=a^{mn}$

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

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

$=\sqrt[4]{\sqrt[3]{4}}\\=\sqrt[4]{4^{1/3}}\\\\=(4^{1/3})^{1/4}\\\\=4^{1/3.1/4}\\\\=4^{1/12}\\\\=(2^{2})^{12}\\\\=2^{1/6}$

The correct answer is $=2^{1/6}$.

#SPJ2