Respuesta :
The roots of same index and the values inside roots are real numbers, thus they can be combined under single root.
The product of given expression will be [tex]6\:^3\sqrt{5}[/tex]
Given that:
- To find the product [tex]^3\sqrt{24}\: \times\: ^3\sqrt{45}[/tex]
Evaluation:
Since both 24 and 45 are real numbers and since the root is of 3 index, thus we can combine both operands under multiplication under cube root.
Thus, we will have:
[tex]\begin{aligned}^3\sqrt{24}\: \times\: ^3\sqrt{45} &=\: ^3\sqrt{24 \times 45} \\&= \: ^3\sqrt{4 \times 6 \times 15 \times 3}\\&= \: ^3\sqrt{2^3 \times 3^3 \times 5}\\&= 2 \times 3 \times \: ^3\sqrt{5}\\&= 6\:^3\sqrt{5}\end{aligned}[/tex]
Thus, the product result would be [tex]6\:^3\sqrt{5}[/tex]
Learn more about cube root related products here:
https://brainly.com/question/22376721
