Rewrite the irrational cube root root(48, 3) as a product of an integer and another irrational cube root.
O 2 * root(6, 3)
O 4 * root(3, 3)
O - 2 * root(6, 3)
(1 point)
O 4 * root(12, 3)
The correct answer is O 2 * root(6, 3).
To rewrite the irrational cube root root(48, 3) as a product of an integer and another irrational cube root, we need to find a perfect cube that divides 48.
48 can be divided by 8, which is a perfect cube. So, we can rewrite root(48, 3) as root(8 * 6, 3).
Taking the cube root of 8, we get 2. Therefore, root(8, 3) is equal to 2.
Hence, root(48, 3) can be written as 2 * root(6, 3).
To rewrite the irrational cube root ∛48 as a product of an integer and another irrational cube root, we can simplify the number by factoring out perfect cube numbers.
First, let's simplify 48 by finding its prime factors:
48 = 2 * 2 * 2 * 2 * 3
Now, let's separate the perfect cubes from the remaining factors:
48 = (2 * 2 * 2) * (2 * 3)
= 2^3 * (2 * 3)
= 2^3 * 6
So, we have the cube root of 48 written as:
∛48 = ∛(2^3 * 6)
Now, we can rewrite this as a product:
∛48 = ∛2^3 * ∛6
Simplifying the cube root of 2^3, we get:
∛2^3 * ∛6 = 2 * ∛6
Hence, the irrational cube root ∛48 can be rewritten as 2 * ∛6.
To rewrite the irrational cube root ∛48 as a product of an integer and another irrational cube root, we need to factorize 48 into the product of a perfect cube and another number.
To do this, let's break down 48 into its prime factors: 48 = 2^4 * 3.
Now, we can look for a perfect cube among these prime factors. In this case, we see that 8 = 2^3 is a perfect cube.
So we can rewrite 48 as 48 = 8 * 2 * 3.
Now, we can rewrite the original expression: ∛48 = ∛(8 * 2 * 3).
Since the cube root of 8 is a perfect cube (2), we can rewrite the expression as:
∛48 = 2 * ∛(2 * 3).
Simplifying further, we have:
∛48 = 2 * ∛6.
Therefore, the irrational cube root ∛48 can be expressed as the product of an integer (2) and another irrational cube root (∛6).
So, the correct answer is 2 * ∛6.