What is the irrational cube root of ^3√81 rewritten as a product of an integer and another irrational cube root?
The cube root of 81 is 4. So, we want to find an expression for the cube root of 81 as a product of an integer and an irrational cube root.
Since the cube root of 81 is 4, we can rewrite it as:
^3√81 = 4 * (^3√1) = 4 * 1 = 4
So, the irrational cube root of 81, ^3√81, can be rewritten as the product of an integer (4) and another irrational cube root (√1).
To find the irrational cube root of ^3√81 rewritten as a product of an integer and another irrational cube root, we can factorize 81 into its prime factorization.
The prime factorization of 81 is 3^4.
Now, we can rewrite ^3√81 as ^3√(3^4).
Taking the cube root, we will have:
^3√(3^4) = 3^(4/3)
Now, we rewrite 3^(4/3) as a product of an integer and another irrational cube root:
3^(4/3) = (3^1)^(4/3) = 3^(1/3 * 4)
So, the answer is 3^(1/3 * 4), which can be written as:
3 * ^3√(3^4)
Therefore, the irrational cube root of ^3√81 rewritten as a product of an integer and another irrational cube root is 3 * ^3√(3^4).
To find the irrational cube root of ^3√81 and rewrite it as a product of an integer and another irrational cube root, we first need to simplify the cube root of 81.
The cube root of 81 can be found by taking the cube root of both the numerator and the denominator of the fraction 81/1.
The cube root of 81 is 4 because 4^3 = 64.
So, ^3√81 = 4.
To rewrite this as a product of an integer and another irrational cube root, we can write it as 4 * ^3√1.
Since the cube root of 1 is 1, ^3√1 can be simplified to 1.
So, the irrational cube root of ^3√81 can be rewritten as 4 * ^3√1.
Therefore, the irrational cube root of ^3√81 can be written as 4 * ^3√1 or simply 4.