Rewrite the irrational cube root ^3√48 as a product of an integer and another irrational cube root.
1. 4 ^3√3
2. 4 ^3√12
3. -2 ^3√6
4. 2 ^3√6
1. The irrational cube root ^3√48 can be written as 4 * ^3√3.
2. The irrational cube root ^3√48 can be written as 4 * ^3√12.
3. The irrational cube root ^3√48 can be written as -2 * ^3√6.
4. The irrational cube root ^3√48 can be written as 2 * ^3√6.
which one is right bot?
My apologies for the oversight in my previous response. Let me correct it:
1. The irrational cube root ^3√48 cannot be written as 4 * ^3√3.
2. The irrational cube root ^3√48 can be written as 2 * ^3√12.
3. The irrational cube root ^3√48 cannot be written as -2 * ^3√6.
4. The irrational cube root ^3√48 cannot be written as 2 * ^3√6.
1. The irrational cube root of 48 can be written as the product of an integer and another irrational cube root as follows:
^3√48 = ^3√(4 * 12)
So, we can rewrite it as:
^3√48 = 4 * ^3√12
2. The irrational cube root of 48 can also be written as:
^3√48 = ^3√(4 * 12)
So, we can rewrite it as:
^3√48 = 4 * ^3√12
3. The irrational cube root of 48 can be written as:
^3√48 = ^3√(8 * 6)
So, we can rewrite it as:
^3√48 = 2 * ^3√6
4. The irrational cube root of 48 can be written as:
^3√48 = ^3√(8 * 6)
So, we can rewrite it as:
^3√48 = 2 * ^3√6
To rewrite the irrational cube root ^3√48 as a product of an integer and another irrational cube root, we need to find a perfect cube (integer) that can be factored out of 48.
1. Let's start with the first option: 4 ^3√3. This is not correct because 4 is not a factor of 48.
2. Next, we have 4 ^3√12. This is also not correct because 4 is not a factor of 48, and 12 is not a perfect cube.
3. The third option is -2 ^3√6. This is incorrect because -2 is not a factor of 48.
4. Lastly, we have 2 ^3√6. This is the correct answer. Let's go through the steps to verify it:
- We can rewrite 48 as 2 * 2 * 2 * 2 * 3, or 2^4 * 3.
- Taking the cube root of 2^4 * 3, we can simplify it as (2^3 * 2) ^3√3.
- This can be further simplified as 2 ^3√3.
Therefore, the correct answer is:
^3√48 = 2 ^3√6.