Find the cube root of 512: ^3√512
1. -8
2. 8
3. 170.666...
4. 8, -8
The correct answer is 2. 8
To find the cube root of 512, we can use the fact that the cube root of a number is the number that, when multiplied by itself three times, equals the original number.
To solve this, we need to find a number that, when multiplied by itself three times, equals 512.
Let's check the options:
1. -8: (-8) x (-8) x (-8) = -512, so this is not the correct answer.
2. 8: (8) x (8) x (8) = 512, so this is the correct answer.
3. 170.666...: (170.666...) x (170.666...) x (170.666...) is approximately equal to 512, so this is not the exact answer.
4. 8, -8: We only need one cube root answer, so this is not the correct answer.
Therefore, the correct answer is option 2: 8.
To find the cube root of 512, you need to calculate the number that, when multiplied by itself twice, equals 512.
One way to find the cube root is by using prime factorization. Start by finding the prime factors of 512:
512 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 (or 2^9)
Next, group the prime factors in triples:
512 = (2 * 2 * 2) * (2 * 2 * 2) * (2 * 2 * 2)
Simplifying, we get:
512 = 8 * 8 * 8
So, the cube root of 512 is 8.
Hence, the correct answer is option 2: 8.