Find the cube root of 512: 512−−−√3
The cube root of 512 is 8.
To find the cube root of 512 (512^(1/3)), follow these steps:
Step 1: Start with the number 512.
Step 2: Divide 512 by different numbers until you find a perfect cube. Let's try dividing it by 2.
512 ÷ 2 = 256
Step 3: Divide the result from the previous step by the same number used before.
256 ÷ 2 = 128
Step 4: Repeat step 3 until you reach a number that you can't divide evenly.
128 ÷ 2 = 64
64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1
Step 5: The last result (1) is a perfect cube. Therefore, the cube root of 512 is 2.
Thus, the cube root of 512 is 2.
To find the cube root of 512, you can use a calculator or do it manually by following these steps:
1. Take the number you want to find the cube root of, which is 512 in this case.
2. Start with an initial guess for the cube root. Let's start with the number 8.
3. Cube the initial guess. 8^3 = 512.
4. Check if the cube of your guess matches the number you want to find the cube root of. Since 8^3 = 512, we have found the cube root.
So, the cube root of 512 is 8.