Question
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Tutor-Verified Answer
Answer
\( \square = -4 \)
Solution
1. Let \( x = \square \). Then the equation becomes:
\[
x^3 = -64
\]
2. To solve for \( x \), take the cube root of both sides:
\[
x = \sqrt[3]{-64}
\]
3. Recognize that the cube root of a negative number is the negative of the cube root of the positive number:
\[
\sqrt[3]{-64} = -\sqrt[3]{64}
\]
4. Since \( \sqrt[3]{64} = 4 \) (because \( 4^3 = 64 \)):
\[
x = -4
\]
5. Verification:
\[
(-4)^3 = -64
\]
Therefore, the solution is:
\[
\square = -4
\]
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Simplify this solution Bonus Knowledge
To solve \( \square^{3} = -64 \), you’ll want to find the cube root of -64. This can be expressed as \( \square = \sqrt[3]{-64} \). The cube root of -64 is -4, because \((-4) \times (-4) \times (-4) = -64\). So, the solution is \( \square = -4 \). When working with cube roots, keep in mind that negative numbers have real cube roots. Unlike square roots that involve imaginary numbers for negatives, cube roots let us embrace the negatives and find that charming solution without any convoluted business! So in this case, don’t shy away from the negative—it’s your friend!
