What is the irrational cube root √16 3
rewritten as
a product of an integer and another irrational cube
root?
To rewrite the irrational cube root √16 3 as a product of an integer and another irrational cube root, we can first simplify the expression.
√16 3 can be rewritten as (∛16)^(1/3).
We know that the cube root of 16 is 2, as 2^3 = 16.
Thus, (∛16)^(1/3) can be simplified to 2^(1/3).
Therefore, √16 3 rewritten as a product of an integer and another irrational cube root is 2^(1/3).
To rewrite the irrational cube root √16 3 as a product of an integer and another irrational cube root, we need to find a perfect cube factor of 16.
First, let's find the prime factorization of 16: 16 = 2^4.
Now, we can see that 2^3, which is 8, is a perfect cube factor of 16.
So, we can rewrite √16 as √(8 × 2) or √8 × √2.
The cube root of 8 can be simplified as 2∛2, as the cube root of 8 = ∛(2^3) = 2∛2.
Therefore, the irrational cube root √16 3 can be rewritten as 2∛2 × √2.
To rewrite the irrational cube root √16 3 as a product of an integer and another irrational cube root, we can simplify it.
First, let's find the cube root of 16:
∛16 = 2
Therefore, we can rewrite the cube root of 16 as:
∛16 = 2∛1
Now, let's focus on the irrational cube root √3:
To rewrite this as a cube root, we need to determine the equivalent expression of √3 in terms of a cube root.
Notice that √3 is equivalent to (∛9/∛3) since 3 is equal to 9/3.
So, we can rewrite √3 as ∛9/∛3.
Putting it all together, we have:
√16 3 = 2∛1 * ∛9/∛3
Therefore, the irrational cube root √16 3 can be rewritten as a product of an integer and another irrational cube root as 2∛1 * ∛9/∛3.