Question

What is ^3 √-72 simplified? Note: You will find the option to add a cubic root symbol in the Algebra (×) keyboard.

Answer 1

To simplify \( \sqrt[3]{-72} \), we first break down \(-72\) into its factors.

1. Write \(-72\) as:
\[
-72 = -1 \times 72
\]
Next, we can express \(72\) in terms of its prime factors:
\[
72 = 8 \times 9 = 8 \times 3^2 = 2^3 \times 3^2
\]
Therefore, we can write:
\[
-72 = -1 \times 2^3 \times 3^2
\]

2. Now we apply the cube root to each factor:
\[
\sqrt[3]{-72} = \sqrt[3]{-1 \times 2^3 \times 3^2}
\]
We can separate the cube roots:
\[
\sqrt[3]{-1} \times \sqrt[3]{2^3} \times \sqrt[3]{3^2}
\]

3. Calculate each term:
- \( \sqrt[3]{-1} = -1 \)
- \( \sqrt[3]{2^3} = 2 \)
- \( \sqrt[3]{3^2} \) cannot be simplified further and is left as \( \sqrt[3]{9} \).

4. Putting it all together:
\[
\sqrt[3]{-72} = -1 \times 2 \times \sqrt[3]{9} = -2 \sqrt[3]{9}
\]

Thus, the simplified form of \( \sqrt[3]{-72} \) is:
\[
\boxed{-2 \sqrt[3]{9}}
\]