simplify 3 square root of 27

To simplify \(3 \sqrt{27}\), first, simplify the square root of 27.

We can break it down as follows:

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

Now, substitute back into the expression:

\[ 3 \sqrt{27} = 3 \cdot (3\sqrt{3}) = 9\sqrt{3} \]

Thus, the simplified form of \(3 \sqrt{27}\) is:

\[ \boxed{9\sqrt{3}} \]

If you're looking to express \(3 \sqrt{27}\) as a single numerical value, we first calculate the square root and then multiply.

1. Simplify \( \sqrt{27} \): \[ \sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3} \]

2. Now calculate \(3 \times \sqrt{27}\): \[ 3 \sqrt{27} = 3 \times 3\sqrt{3} = 9\sqrt{3} \]

3. If you want a numerical approximation, calculate \( \sqrt{3} \) (which is approximately 1.732): \[ 9\sqrt{3} \approx 9 \times 1.732 \approx 15.588 \]

Thus, \(3 \sqrt{27}\) as a single numerical value (approximately) is:

\[ \boxed{15.588} \]