ANSWER
[tex]40xy\sqrt[]{21}[/tex]
EXPLANATION
We want to simplify the radical expression given:
[tex](5\sqrt[]{2y})(4\sqrt[]{7xy})(\sqrt[]{6x})[/tex]
First, separate the terms outside the radicals and the terms inside the radicals:
[tex]5\cdot4\cdot\sqrt[]{2y}\cdot\sqrt[]{7xy}\cdot\sqrt[]{6x}[/tex]
Since all the radicals are square roots, we can multiply all the terms inside the radicals:
[tex]5\cdot4\cdot\sqrt[]{2y\cdot7xy\cdot6x}[/tex]
Simplify:
[tex]20\cdot\sqrt[]{84\cdot x^2\cdot y^2}[/tex]
Now, express the terms in the radicals as a product of their factors in order to simplify:
[tex]\begin{gathered} 20\cdot\sqrt[]{2\cdot2\cdot3\cdot7\cdot x\cdot x\cdot y\cdot y} \\ 20\cdot\sqrt[]{2^2\cdot3\cdot7\cdot x^2\cdot y^2} \end{gathered}[/tex]
Simplify by finding the square root of factors that are repeated in the square root:
[tex]\begin{gathered} 20\cdot2\cdot x\cdot y\cdot\sqrt[]{3\cdot7} \\ \Rightarrow40xy\sqrt[]{21} \end{gathered}[/tex]
That is the answer.
