Question

What is −72−−−−√3 simplified?

Note: You will find the option to add a cubic root symbol in the Algebra (×) keyboard.

(1 point)

Answer 1

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!