Question

Combine and simplify the following radical expresión.

Answer 1

12(3√6)

Explanation:

6(3√12)(3√2)

= 6(3√4√3)(3√2)

= 12(3√3)(3√2)

= 12(3√6)

Answer 2

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

Explanation:

It is important to remember that:

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

2)
`\sqrt[n]{a^n} =a^(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}`