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

1 Answer

4 votes

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.

User SeanWM
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