Rewrite the irrational cube root 48−−√3 as a product of an integer and another irrational cube root.(1 point)
Responses
26–√3
2 root index 3 start root 6 end root
43–√3
4 root index 3 start root 3 end root
412−−√3
4 root index 3 start root 12 end root
−26–√3
negative 2 root index 3 start root 6 end root
The irrational cube root of 48 can be expressed as 2√3 root 3.
Rewrite the irrational cube root 48−−√3 as a product of an integer and another irrational cube root.(1 point)
Responses
26–√3
43–√3
412−−√3
−26–√3
The irrational cube root of 48 can be expressed as 4√3 root 3.
To rewrite the irrational cube root ∛48 as a product of an integer and another irrational cube root, we can simplify it by factoring out the perfect cubes from the 48.
1. First, we need to find the perfect cube that can be factored out from 48. The largest perfect cube that is a factor of 48 is 8, which is equal to (2^3).
2. Next, we can rewrite 48 as (2^3 * 6). This means that ∛48 can be rewritten as ∛(2^3 * 6).
3. Using the property of cube roots (∛a * b = ∛a * ∛b), we can split ∛(2^3 * 6) into ∛2^3 * ∛6.
4. Simplifying this, we get 2 * ∛6.
Therefore, the irrational cube root ∛48 can be rewritten as a product of the integer 2 and another irrational cube root ∛6.