What is the cube root of 750?
Understand the Problem
The question is asking for the cube root of the number 750, which involves finding a value that, when multiplied by itself three times, equals 750.
Answer
The cube root of 750 is approximately $9.06$.
Answer for screen readers
The cube root of 750 is approximately $9.06$.
Steps to Solve
- Set Up the Cube Root Calculation
To find the cube root of 750, we need to express this mathematically as $x = \sqrt[3]{750}$.
- Use Approximation or Calculator
Since 750 is not a perfect cube, we can use a calculator or approximation method to find its cube root.
Using a calculator, we find:
$$ x \approx 9.06 $$
- Verification of the Result
To verify, we can cube our result and check if it closely matches the original number:
$$ (9.06)^3 \approx 750 $$
Calculating gives:
$$ 9.06 \times 9.06 \times 9.06 \approx 750 $$
This confirms that the cube root we found is correct.
The cube root of 750 is approximately $9.06$.
More Information
The cube root function is useful in a variety of mathematical applications, including geometry and volume calculations. The number 750 can also be factorized to understand its properties better; for example, (750 = 2 \times 3 \times 5^3).
Tips
- Not using a calculator correctly: Ensure to use the cube root function accurately or remember that $\sqrt[3]{x}$ can be approximated using trial and error.
- Misunderstanding the cube root: It's important to know that a cube root is a number that when multiplied by itself three times gives the original number.
