Question

cubed √-72 simplified

Answer 1

To simplify the expression \(\sqrt[3]{-72}\), we can start by factoring \(-72\).

First, we can rewrite \(-72\) as:

\[
-72 = -1 \times 72
\]

Next, we can further factor \(72\):

\[
72 = 8 \times 9 = 8 \times (3^2)
\]

Since \(8\) is a perfect cube (\(2^3\)), we can express \(-72\) as:

\[
-72 = -1 \times 2^3 \times 3^2
\]

Now we can use the property of cube roots that states:

\[
\sqrt[3]{a \times b} = \sqrt[3]{a} \times \sqrt[3]{b}
\]

Applying this to our expression, we have:

\[
\sqrt[3]{-72} = \sqrt[3]{-1} \times \sqrt[3]{2^3} \times \sqrt[3]{3^2}
\]

Calculating each component:

- \(\sqrt[3]{-1} = -1\)
- \(\sqrt[3]{2^3} = 2\)
- \(\sqrt[3]{3^2} = 3^{2/3} = 3^{2/3} = \sqrt[3]{9}\)

Now we can combine these results:

\[
\sqrt[3]{-72} = -1 \times 2 \times \sqrt[3]{9} = -2 \sqrt[3]{9}
\]

So, the simplified form of \(\sqrt[3]{-72}\) is:

\[
\sqrt[3]{-72} = -2 \sqrt[3]{9}
\]