Question
Real Tutor Solution
Tutor-Verified Answer
Answer
The cube root of \(-125\) is \(-5\).
Solution
To find the cube root of \(-125\), we can express it mathematically as:
\[
\sqrt[3]{-125}
\]
The cube root of a negative number is also negative. We can find the cube root of \(125\) first:
\[
\sqrt[3]{125} = 5
\]
Since we are looking for the cube root of \(-125\), we take the negative of the cube root of \(125\):
\[
\sqrt[3]{-125} = -\sqrt[3]{125} = -5
\]
Thus, the cube root of \(-125\) is:
\[
\boxed{-5}
\]
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Simplify this solution Beyond the Answer
The cube root of \( -125 \) is \( -5 \). This is because when you multiply \( -5 \) by itself three times, you get \( -125 \) (that is, \( -5 \times -5 \times -5 = -125 \)). So, while positive numbers can sometimes cause confusion, negative numbers have the exciting ability to yield cube roots that are also negative! Fun fact: Understanding cube roots can be super useful in various fields such as architecture and engineering, where calculating volume and dimensions plays a crucial role. Need to find the side length of a cube with a volume of \( -125 \) cubic units? Just take the cube root, and you'll be able to design structures that are both fascinating and functional!
