Question

What is the expression in simplified form 5 √ 2 •9 √6

Answer 1

To solve the exercise first, rewrite √6

`\sqrt[]{6}=\sqrt[]{2\cdot3}`

Now, apply this law of radicals

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

Then, you have

`5\sqrt[]{2}\cdot9\sqrt[]{6}=5\sqrt[]{2}\cdot9\sqrt[]{2}\cdot\sqrt[]{3}`

Now, apply this law of radicals

`\begin{gathered} \sqrt[]{a}\cdot\sqrt[]{a}=a \\ \text{ Then} \\ \sqrt[]{2}\cdot\sqrt[]{2}=2 \end{gathered}`

Finally, you have

`\begin{gathered} 5\sqrt[]{2}\cdot9\sqrt[]{6}=5\sqrt[]{2}\cdot9\sqrt[]{2}\cdot\sqrt[]{3} \\ 5\sqrt[]{2}\cdot9\sqrt[]{6}=5\cdot9\cdot2\sqrt[]{3} \\ 5\sqrt[]{2}\cdot9\sqrt[]{6}=90\sqrt[]{3} \end{gathered}`

Therefore, the simplified form of the given expression is

`90\sqrt[]{3}`

and the correct and answer is option D.