Question

Simplify: $\sqrt[3]{316}+\sqrt[3]{354}+\sqrt[3]{3192}-\sqrt[3]{3375}$

Answer 1

$16=2^4=2\left(2^3\right)$
$54=2\left(3^3\right)$
$192=3\cdot 2^6=3(4{)}^3$
$375=3\left(5^3\right)$

$\therefore (16{)}^{\frac{1}{3}}+(54{)}^{\frac{1}{3}}+(192{)}^{\frac{1}{3}}-(375{)}^{\frac{1}{3}}=\left[2\right(2^3){]}^{\frac{1}{3}}+[2\left(3^3\right){]}^{\frac{1}{3}}+\left[3\right(4{)}^3{]}^{\frac{1}{3}}+\left[3\right(5^3){]}^{\frac{1}{3}}$
$=2\left(2^{\frac{1}{3}}\right)+3\left(2^{\frac{1}{3}}\right)+4(3{)}^{\frac{1}{3}}-5(3^{\frac{1}{3}})$ Using the rule of $(a^m{)}^n=a^{m\times n}$

$=5\left(2^{\frac{1}{3}}\right)-\left(3^{\frac{1}{3}}\right)$