Understanding Cube Roots
Cube roots are a way to determine what number, when multiplied by itself three times, equals a specific value. For example, the cube root of a number x is a number y such that y * y * y = x.
Finding the Cube Root of 729
To determine if 9 is the cube root of 729, we need to compute:
- 9 * 9 * 9
Calculating this step-by-step:
- First, calculate 9 * 9 = 81
- Then, multiply 81 by 9:
- 81 * 9 = 729
Since 9 * 9 * 9 equals 729, we confirm that:
- The cube root of 729 is indeed 9.
Evaluating Other Options
Let's briefly look at the other options to clarify why they are incorrect:
- 343:
- Cube root calculation: 7 * 7 * 7 = 343, so the cube root is 7.
- 629:
- Cube root calculation: The cube root of 629 is not a whole number.
- 81:
- Cube root calculation: 4 * 4 * 4 = 64 (not equal to 81).
Conclusion
The correct answer to the question "9 is the cube root of __________" is option 'B', which is 729. This confirms that the value of 729 can be expressed as 9 raised to the power of 3.