what is the irrational cube root 3√40 rewritten as a product of an integer and another irrational cube root
To rewrite the irrational cube root ∛40 as a product of an integer and another irrational cube root, we first need to find a perfect cube factor of 40.
The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40.
However, none of these factors are perfect cubes.
Now, let's calculate the cube root of 40: ∛40 ≈ 3.107
Since 40 is not a perfect cube, ∛40 is an irrational number. It cannot be rewritten as a product of an integer and another irrational cube root.
do it right
I apologize for my previous mistake. Let's correct it.
To rewrite the irrational cube root ∛40 as a product of an integer and another irrational cube root, we need to find a perfect cube factor of 40.
The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40.
The largest perfect cube factor of 40 is 8, which is equal to 2^3.
So, we can rewrite ∛40 as ∛(8×5).
This can be further simplified as 2∛5.
Therefore, the irrational cube root ∛40 can be rewritten as a product of an integer (2) and another irrational cube root (∛5).
To rewrite the irrational cube root ∛40 as a product of an integer and another irrational cube root, we can start by factoring 40.
First, let's find the prime factors of 40:
40 = 2 * 2 * 2 * 5
Next, we can rewrite 40 as a product of perfect cube factors:
40 = (2 * 2 * 2) * (5)
Now, we need to group the perfect cube factors together:
40 = 8 * 5
So, the irrational cube root ∛40 can be rewritten as:
∛40 = ∛(8 * 5)
Now, we can take the cube root of the perfect cube factor, 8:
∛40 = (∛8) * ∛5
The cube root of 8 is 2:
∛40 = 2 * ∛5
Therefore, the irrational cube root ∛40 can be rewritten as the product of the integer 2 and the irrational cube root ∛5.
To rewrite the irrational cube root ∛40 as a product of an integer and another irrational cube root, we need to factorize the number 40.
First, find the prime factorization of 40: 40 = 2^3 * 5.
Now, we will look for perfect cube factors. In this case, the factor 8 (2^3) is a perfect cube.
∛40 can be written as ∛(8 * 5).
Using the property of cube roots, we can separate the perfect cube factor from the remaining factor: ∛(8 * 5) = ∛8 * ∛5.
Since ∛8 = 2 and ∛5 remains as an irrational cube root, we can rewrite ∛40 as 2∛5.
Therefore, the irrational cube root ∛40 can be expressed as the product of an integer and another irrational cube root: 2∛5.