Question

State True or False.

$\sqrt[5]{5\sqrt[4]{4{\left(2^4\right)}^3}}-5\sqrt[5]{58}+2\sqrt[5]{5\sqrt[4]{4{\left(2^3\right)}^4}}$$=-2\cdot \sqrt[5]{58}$

• A. True
• B. False

Answer 1

The correct option is A True

As given $\sqrt[5]{5\sqrt[4]{4{\left(2^4\right)}^3}}-5\sqrt[5]{58}+2\sqrt[5]{5\sqrt[4]{4{\left(2^3\right)}^4}}$
$={\left({\left(2^{12}\right)}^{\frac{1}{4}}\right)}^{\frac{1}{5}}-5{\left(2^3\right)}^{\frac{1}{5}}+2{\left({\left(2^{12}\right)}^{\frac{1}{4}}\right)}^{\frac{1}{5}}$
$={\left(2^3\right)}^{\frac{1}{5}}-5\left(2^{\frac{3}{5}}\right)+2{\left(2^3\right)}^{\frac{1}{5}}$
$=2^{\frac{3}{5}}-5\left(2^{\frac{3}{5}}\right)+2\left(2^{\frac{3}{5}}\right)$
$=2^{\frac{3}{5}}(1-5+2)$
$=-2\cdot 2^{\frac{3}{5}}$
$-2\cdot {\left(2^3\right)}^{\frac{1}{5}}$
$=-2\cdot \sqrt[5]{58}$