Find the cube root of 512: 512−−−√3.(1 point)
Responses
8
8
170.666...
170.666...
8, −8
8 comma negative 8
−8
The cube root of 512 is 8.
To find the cube root of 512, we need to find the number that, when multiplied by itself three times, gives us 512.
The cube root of 512 is 8, which means 8 * 8 * 8 = 512.
So, the answer is 8.
To find the cube root of 512, you can use a calculator that has a cube root function. However, if you don't have access to a calculator or want to understand the process, you can find the cube root manually.
To manually find the cube root of a number, you can use a method called prime factorization. Here's how you can do it for 512:
1. Decompose 512 into its prime factors: 512 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 2^9
2. Group the prime factors in sets of three: 2^9 can be grouped as (2^3)^3
3. The cube root of 512 is equal to the product of the cubed root of each group: cube root of (2^3)^3
cube root of 2^3 = 2
4. Simplify the expression: cube root of (2^3)^3 = 2^3 = 8
Therefore, the cube root of 512 is 8.