Dividing the following radical expression: \$ (6\sqrt((2)\sqrt(3))) / (\sqrt(6))\$.

The given radical expression is

\$ (6\sqrt((2)\sqrt(3))) / (\sqrt(6))\$

Simplify first \$\sqrt(6)\$:

\$\sqrt(6) = \sqrt(2 .3) = \sqrt(2) . \sqrt(3)\$

Substitute and simplify the numerator \$ 6\sqrt((2) \sqrt(3))\$:

\$6 \(sqrt((2). (3)^(1/2))) = 6 (2 .3^(1/2))^(1/2)\$

\$6 . 2^(1/2) . (3^(1/2))^(1/2) = 6 . 2^(1/2). 3^(1/4)\$

Combine and simplify:

\$ (6\sqrt((2)\sqrt(3))) / (\sqrt(6)) = (6. 2^(1/2). 3^(1/4)) / (\sqrt(2) . \sqrt(3))\$

\$= (6 . 3^(1/4)) / (3^(1/2))\$

\$= 6 . 3^(1/4 - 1/2)\$

\$= 6 . 3^(- 1/4)\$

\$= 6 / 3^(1/4)\$

Make it simplify

\$(2 . 3) / 3^ (1/4)\$

\$2 root(4) (3^3)\$

So, therefore the simplified expression is \$ 2 root(4) (3^3)\$.

It is missing the factor of 2, which is necessary for correctly simplifying the original expression. Hence, option A is not equivalent to the given expression

\$ root(4)(3^3)\$

Option B suggests \$ 2 root(3)(4^3)\$ which involves a cube root and \$4^3\$ whereas the simplified form involves a fourth root and \$3^3\$

\$ 2 root(3)(4^3)\$

Option C is correct: It accurately simplifies the division of radicals given in the original expression

\$ 2 root(4)(3^3)\$

It does not represent the correct simplification based on the rules of dividing radicals

\$ root(3)(4^3)\$

Option

C

Can you summarize what you’ve understood in the above steps?