Simplify \(\sqrt{27}\) + \(\frac{3}{\sqrt{3}}\)

  • A 4\(\sqrt{3}\)
  • B \(\frac{4}{\sqrt{3}}\)
  • C 3\(\sqrt{3}\)
  • D \(\frac{\sqrt{3}}{4}\)

The correct answer is A. 4\(\sqrt{3}\)

The correct answer is **A. 4\(\sqrt{3}\)**. Here's how to solve the problem:

First, we can simplify \(\sqrt{27}\) by factoring out a perfect square from 27:

\[\sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3}\]

Next, we can simplify \(\frac{3}{\sqrt{3}}\) by rationalizing the denominator:

\[\frac{3}{\sqrt{3}} = \frac{3}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{3\sqrt{3}}{3} = \sqrt{3}\]

Adding the two simplified expressions together, we get:

\[3\sqrt{3} + \sqrt{3} = 4\sqrt{3}\]

So, the simplified form of the expression is **4\(\sqrt{3}\)**.

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