Is 8 a perfect cube?
Understand the Problem
The question is asking whether the number 8 can be expressed as the cube of an integer. A perfect cube is a number that can be written as a^3, where a is an integer.
Answer
Yes, $8 = 2^3$.
Answer for screen readers
Yes, the number 8 can be expressed as the cube of the integer 2, since $2^3 = 8$.
Steps to Solve
- Identify the integer possibilities for cubes
To determine if 8 is a perfect cube, we need to check if there is any integer $a$ such that $a^3 = 8$.
- Calculate the cube root
We can express this mathematically as finding $a$: $$ a = \sqrt[3]{8} $$
- Evaluate the cube root
Now we calculate the cube root of 8: $$ a = 2 $$
- Verify the result
Lastly, we verify our calculation by cubing the result: $$ 2^3 = 2 \times 2 \times 2 = 8 $$
Since the calculation holds true, we can conclude that 8 is indeed a perfect cube.
Yes, the number 8 can be expressed as the cube of the integer 2, since $2^3 = 8$.
More Information
The only integers whose cubes equal 8 are positive and negative versions of the cube root, which in this case is 2. A fun fact is that perfect cubes can be visually represented as the volume of a cube with side lengths equal to the integer.
Tips
One common mistake is assuming that a number has to be positive to be a perfect cube. Remember, both positive and negative integers can be cubed.
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