To simplify \( -72\sqrt{3} \), we can look for a common way to rewrite the expression or isolate terms.
First, \( -72 \) can be expressed as:
\[ -72 = -36 \times 2 \]
Thus:
\[ -72\sqrt{3} = -36\sqrt{3} \times 2 \]
Next, since we notice that \( -36 \) is a perfect square, we can rewrite it:
\[ -36 = -1 \times 36 = -1 \times 6^2 \]
This gives us:
\[ -72\sqrt{3} = -1 \times 6^2 \times 2\sqrt{3} = -6^2 \times 2\sqrt{3} \]
However, if you meant \( -72 \) to be the cube root instead of the square root in your expression (as noted by your reference to a cubic root), we may consider \( -72 \) taking a cubic root:
The expression could imply the cubic root of -72 multiplied by \( \sqrt{3} \):
\[ \sqrt[3]{-72} \cdot \sqrt{3} \]
The cubic root of -72 can be simplified as:
\[ \sqrt[3]{-72} = \sqrt[3]{-1 \cdot 72} = -\sqrt[3]{72} \]
Now, finding the prime factorization of 72 we get:
\[ 72 = 8 \times 9 = 2^3 \times 3^2 \]
So:
\[ \sqrt[3]{72} = \sqrt[3]{2^3 \cdot 3^2} = 2 \sqrt[3]{3^2} = 2\sqrt[3]{9} \]
Thus, putting it all together:
\[ \sqrt[3]{-72} = -2 \sqrt[3]{9} \]
If we multiply that by \( \sqrt{3} \):
\[ -2 \sqrt[3]{9} \cdot \sqrt{3} \]
This expression doesn't simplify further neatly without approximating values.
If the original \( -72\sqrt{3} \) was entirely meant as is, then the answer remains:
\[ -72 \sqrt{3} \]
If it was meant to evaluate \( \sqrt[3]{-72} \sqrt{3} \), let me know!