What is the irrational cube root −24−−−−√3 rewritten 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 −24–√3 negative 2 root index 3 start root 4 end root 23–√3 2 root index 3 start root 3 end root −23–√3
The irrational cube root −24−−−−√3 can be rewritten as −2∛6.
To rewrite the irrational cube root -24√3 as a product of an integer and another irrational cube root, we can proceed as follows:
1. Write -24 as a product of its prime factors: -24 = -1 × 2 × 2 × 2 × 3.
2. Identify any perfect cube factors. In this case, we have 2 × 2 × 2 = 2^3 = 8, which is a perfect cube.
3. Rewrite the given expression using the perfect cube factor and the remaining factors as a separate cube root:
-24√3 = -8√3 × 3.
So, the irrational cube root -24√3 can be rewritten as -8√3 × 3, where -8√3 is the integer part and 3 is the remaining irrational cube root.
To rewrite the expression −24−−−−√3 as a product of an integer and another irrational cube root, we need to simplify it.
First, let's simplify the cube root of 24. We know that the cube root of a negative number is negative. So, the cube root of 24 is ∛(24) = 2∛3.
Next, let's rewrite the expression −24−−−−√3 using the simplified cube root:
−24−−−−√3 = -2 * (∛3)
Therefore, the expression −24−−−−√3 can be rewritten as a product of -2 and ∛3.