Rewrite the irrational cube root root(48, 3) as a product of an integer and another irrational cube root. (1 point)
O 2 * root(6, 3)
O 4 * root(3, 3)
O - 2 * root(6, 3)
root(12, 4)
None of the options provided are equivalent to the original expression.
The correct answer is: root(12, 4)
To rewrite the expression ∛48 as a product of an integer and another irrational cube root, we need to find a perfect cube that can be pulled out from 48.
We start by finding the prime factorization of 48, which is 2 * 2 * 2 * 2 * 3. Since we need to extract a cube, we group these prime factors into triples. However, we don't have enough factors of 2 to make a complete cube, so we group two 2's together.
Now, we have (2 * 2) * (2 * 2) * 3. Simplifying this, we get 4 * 4 * 3, which equals 48.
Therefore, we can rewrite ∛48 as 4 * ∛3, where 4 is the integer and ∛3 is an irrational cube root.
So, the correct option is: O 4 * root(3, 3)
To rewrite the irrational cube root ∛48 as a product of an integer and another irrational cube root, we need to find the largest perfect cube that divides 48.
Looking at the prime factorization of 48, we have:
48 = 2^4 * 3
The largest perfect cube that divides 48 is 8 since 8 = 2^3. So, we can rewrite ∛48 as:
∛48 = ∛(8 * 6) = ∛8 * ∛6
Now, we can simplify further by expressing ∛8 as an integer and ∛6 as an irrational cube root:
∛48 = 2 * ∛6
Therefore, the answer is:
O 2 * ∛6