Find the cubic root of 96.
1. 2 ^3√12
2. 2 ^3√7
3. 2√12
4. 4√6
The answer is 2 ^3√12.
To find the cubic root of 96, we can use the following steps:
1. Let's first factorize 96 into prime factors: 96 = 2^5 * 3^1.
2. Now, let's simplify the expression using the properties of exponents. The cubic root can be represented as ^3√(2^5 * 3^1).
3. Using the property of exponents, we can split the root into two separate roots: ^3√(2^3 * 2^2 * 3^1).
4. We can simplify further by taking the cube root of each term separately: 2^3 * ^3√(2^2 * 3^1).
5. Since 2^3 equals 8, the expression becomes 8 * ^3√(2^2 * 3^1).
6. Now, we can simplify the remaining root: ^3√(2^2 * 3^1) = ^3√(4 * 3) = ^3√12.
Therefore, the cubic root of 96 is 8 * ^3√12. So, the correct answer is 1. 2^3√12.
To find the cubic root of 96, you need to find the number that, when multiplied by itself three times, equals 96.
Option 1: 2 ^3√12
This option suggests taking the cubic root of 12 and then multiplying it by 2. However, since 12 is not a perfect cube (i.e., a number that can be evenly divided by an integer three times), this option is not correct.
Option 2: 2 ^3√7
This option suggests taking the cubic root of 7 and then multiplying it by 2. Again, 7 is not a perfect cube, so this option is also not correct.
Option 3: 2√12
This option suggests taking the square root of 12 and then multiplying it by 2. However, we are looking for the cubic root, not the square root, of 96. Thus, this option is not correct.
Option 4: 4√6
This option suggests taking the square root of 6 and then multiplying it by 4. Just like option 3, we are looking for the cubic root, not the square root, of 96. Therefore, this option is also not correct.
In conclusion, none of the given options is the correct way to find the cubic root of 96. Let's try using another method to find the answer.