What is the irrational cube root −24−−−−√3 rewritten as a product of an integer and another irrational cube root?(1 point) Responses −23–√3 negative 2 root index 3 start root 3 end root 23–√3 2 root index 3 start root 3 end root 26–√3 2 root index 3 start root 6 end root −24–√3
The rewritten form of the irrational cube root −24−−−−√3 as a product of an integer and another irrational cube root is 2∛(-3)
To rewrite the irrational cube root −24−−−−√3 as a product of an integer and another irrational cube root, we can simplify the expression as follows:
-24−−−−√3 = (-1) * (8−−−√3)
Therefore, the expression can be rewritten as −23–√3.
To rewrite the irrational cube root −24−−−−√3 as a product of an integer and another irrational cube root, we can first simplify the expression under the cube root sign.
The cube root of a number can be written as follows:
∛(-a) = -∛a when a is a positive number.
In this case, the expression is -∛(24√3).
Next, we can break down 24 into its prime factors.
24 = 2 * 2 * 2 * 3 = 2^3 * 3.
Now, we can rewrite the expression as:
-∛(2^3 * 3 * √3).
Since 2^3 = 8, the expression becomes:
-∛(8 * 3 * √3).
Simplifying further, we get:
-∛(24√3).
Now, we can rewrite this expression as a product of an integer and another irrational cube root:
(-∛24) * (∛√3).
∛24 = 2∛3, so we have:
-2∛3 * (∛√3).
Therefore, the irrational cube root −24−−−−√3 can be rewritten as a product of an integer (-2) and another irrational cube root (∛√3).