What is the cube root of 96?
Understand the Problem
The question is asking for the cube root of 96, which involves finding a number that, when multiplied by itself three times, equals 96.
Answer
The cube root of 96 is approximately $4.64$.
Answer for screen readers
The cube root of 96 is approximately $4.64$.
Steps to Solve
- Set up the equation for the cube root
To find the cube root of 96, we set the equation as follows: $$ x^3 = 96 $$
- Use estimation methods
Since we want $x$, we can estimate by finding two perfect cubes around 96. The cube of 4 is $4^3 = 64$ and the cube of 5 is $5^3 = 125$. This means: $$ 4 < \sqrt[3]{96} < 5 $$
- Refine with a calculator
We can estimate further. We can calculate the cube root approximately using a calculator to find: $$ \sqrt[3]{96} \approx 4.64 $$
- Verification
To verify, we can cube our estimate: $$ 4.64^3 \approx 100.303584 $$ This approximation shows $4.64$ is slightly too high. If we try a lower number, like $4.5$: $$ 4.5^3 = 91.125 $$ This reveals that the cube root lies between $4.5$ and $4.6$.
- Final approximation
Using more decimal places, we conclude: $$ \sqrt[3]{96} \approx 4.64 $$
The cube root of 96 is approximately $4.64$.
More Information
The cube root takes a number and finds a value that, when multiplied by itself three times, gives back the original number. It's common in various fields such as physics, engineering, and computer science where volumetric calculations are needed.
Tips
- Confusing cube roots with square roots; remember that cube roots require multiplication three times.
- Forgetting to check if the estimation lies correct between two perfect cubes can lead to inaccurate answers.
