Question

Combine and simplify the following radical expresión.

Answer 1

Answer: $12\sqrt[3]{3}$

Step-by-step explanation:

It is important to remember that:

1) $(\sqrt[n]{a})(\sqrt[n]{b})=\sqrt[n]{ab}$

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

Knowing this, and given the radical expression $(2\sqrt[3]{12})(3\sqrt[3]{2})$, the procedure is:

Solve the multiplication:

$(2*3)\sqrt[3]{12*2} = 6\sqrt[3]{24}$

Descompose 24 into its prime factors:

$24 = 2*2 *2*3 =2^{3}*3$

Rewriting the radicand and simplifying, we get:

$6\sqrt[3]{2^3*3} = (6)(2)\sqrt[3]{3}= 12\sqrt[3]{3}$

Answer 2

Answer:

12(3√6)

Step-by-step explanation:

6(3√12)(3√2)

= 6(3√4√3)(3√2)

= 12(3√3)(3√2)

= 12(3√6)