Question

May i have guided steps with explanation near each step please. Thanks you

Answer 1

`40xy\sqrt[]{21}`

Step-by-step explanation

We want to simplify the radical expression given:

`(5\sqrt[]{2y})(4\sqrt[]{7xy})(\sqrt[]{6x})`

First, separate the terms outside the radicals and the terms inside the radicals:

`5\cdot4\cdot\sqrt[]{2y}\cdot\sqrt[]{7xy}\cdot\sqrt[]{6x}`

Since all the radicals are square roots, we can multiply all the terms inside the radicals:

`5\cdot4\cdot\sqrt[]{2y\cdot7xy\cdot6x}`

Simplify:

`20\cdot\sqrt[]{84\cdot x^2\cdot y^2}`

Now, express the terms in the radicals as a product of their factors in order to simplify:

`\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}`

Simplify by finding the square root of factors that are repeated in the square root:

`\begin{gathered} 20\cdot2\cdot x\cdot y\cdot\sqrt[]{3\cdot7} \\ \Rightarrow40xy\sqrt[]{21} \end{gathered}`

That is the answer.