What is the cube root of 1/64?
Understand the Problem
The question is asking to find the cube root of the fraction 1/64. This involves determining which number, when multiplied by itself three times, equals 1/64.
Answer
The cube root of $\frac{1}{64}$ is $\frac{1}{4}$.
Answer for screen readers
The cube root of $\frac{1}{64}$ is $\frac{1}{4}$.
Steps to Solve
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Identify the fraction We start with the fraction we need to find the cube root of, which is $\frac{1}{64}$.
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Rewrite the denominator in terms of powers Recognize that $64$ can be expressed as a power of $4$: $$ 64 = 4^3 $$
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Find the cube root of the fraction Now express the fraction in terms of the power we found: $$ \frac{1}{64} = \frac{1}{4^3} $$
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Apply the property of cube roots Using the property of cube roots, we know that the cube root of a fraction can be obtained by taking the cube root of the numerator and the denominator separately: $$ \sqrt[3]{\frac{1}{4^3}} = \frac{\sqrt[3]{1}}{\sqrt[3]{4^3}} $$
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Simplify the cube roots Calculate the cube roots: $$ \sqrt[3]{1} = 1 $$ and $$ \sqrt[3]{4^3} = 4 $$
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Write the final answer Thus, the cube root of $\frac{1}{64}$ is: $$ \frac{1}{4} $$
The cube root of $\frac{1}{64}$ is $\frac{1}{4}$.
More Information
The cube root is a fundamental operation in mathematics that finds a number which, when multiplied by itself three times, gives the original number. In this case, $\frac{1}{4}$ multiplied by itself three times equals $\frac{1}{64}$.
Tips
- Forgetting that the cube root of a fraction involves taking the cube root of the numerator and denominator separately.
- Miscalculating the cube root of numbers, so double-check any calculations involving roots.
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