What is 54−−√3 simplified?

1 answer

To simplify \(54 \sqrt{3}\), we begin by simplifying the component \(54\).

First, let's break down \(54\):

\[ 54 = 18 \times 3 \]

Now, we can express \(54 \sqrt{3}\) as:

\[ 54 \sqrt{3} = (18 \times 3) \sqrt{3} \]

Rearranging gives:

\[ = 18 \sqrt{3} \times 3 = 18 \times \sqrt{3^2} \cdot \sqrt{3} \]

We know that \(\sqrt{3^2} = 3\). Thus we can continue:

\[ = 18 \cdot 3 \cdot \sqrt{3} = 54 \sqrt{3} \]

However, this does not actually simplify our expression, so we consider \(54 \sqrt{3}\) as a product of \(54\) and \(\sqrt{3}\):

Since \(54\) is already a simplified integer and \(\sqrt{3}\) is an irrational number, no further simplification can be performed, and it remains as:

\[ 54 \sqrt{3} \]

Thus, the answer is:

\[ 54 \sqrt{3} \]