Simplify each expression 9 \sqrt{2(4 √(6)) }

Question

Simplify each expression
`9 \sqrt{2(4 √(6)) }`

Answer 1

The expression to simplify is:

`9\sqrt[]{2}(4\sqrt[]{6})`

When we are multiplying two racial expressions, we multiply the constants together and the square roots together. So, the next step is:

`\begin{gathered} 9\sqrt[]{2}(4\sqrt[]{6}) \\ =(9*4)(\sqrt[]{2}*\sqrt[]{6}) \\ =36(\sqrt[]{2}*\sqrt[]{6}) \end{gathered}`

Now, we an use the property

`\sqrt[]{a}*\sqrt[]{b}=\sqrt[]{a* b}`

to simplify it further:

`\begin{gathered} 36(\sqrt[]{2}*\sqrt[]{6}) \\ =36(\sqrt[]{2*6}) \\ =36\sqrt[]{12} \end{gathered}`

We can break apart the square root using the property:

`\sqrt[]{ab}=\sqrt[]{a}\sqrt[]{b}`

So, we have:

`\begin{gathered} 36\sqrt[]{12} \\ =36\sqrt[]{2}\sqrt[]{2}\sqrt[]{3} \end{gathered}`

For the final simplification, we use the property,

`\sqrt[]{a}\sqrt[]{a}=a`

The final answer is:

`\begin{gathered} 36\sqrt[]{2}\sqrt[]{2}\sqrt[]{3} \\ =36(2)\sqrt[]{3} \\ =72\sqrt[]{3} \end{gathered}`Answer
`72\sqrt[]{3}`