Answer: [tex]12\sqrt[3]{3}[/tex]
Step-by-step explanation:
It is important to remember that:
1) [tex](\sqrt[n]{a})(\sqrt[n]{b})=\sqrt[n]{ab}[/tex]
2) [tex]\sqrt[n]{a^n} =a^\frac{n}{n} =a[/tex]
Knowing this, and given the radical expression [tex](2\sqrt[3]{12})(3\sqrt[3]{2})[/tex], the procedure is:
Solve the multiplication:
[tex](2*3)\sqrt[3]{12*2} = 6\sqrt[3]{24}[/tex]
Descompose 24 into its prime factors:
[tex]24 = 2*2 *2*3 =2^{3}*3[/tex]
Rewriting the radicand and simplifying, we get:
[tex]6\sqrt[3]{2^3*3} = (6)(2)\sqrt[3]{3}= 12\sqrt[3]{3}[/tex]
