simplify the cube root of 189.
To simplify the cube root of 189, we need to find the perfect cube that is a factor of 189. The prime factorization of 189 is 3^3 * 7.
Therefore, we can rewrite 189 as (3^3) * 7^(1).
Taking the cube root, we get the simplified form:
³√189 = ³√(3^3 * 7^(1)) = 3 * ³√7.
So, the simplified cube root of 189 is 3 * ³√7.
To simplify the cube root of 189, we need to find the prime factors of 189.
Step 1: Find the factors of 189:
The factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189.
Step 2: Determine the prime factors:
The prime factors of 189 are 3 and 7, as 3 * 7 = 21, and 21 * 9 = 189.
Step 3: Simplify the cube root:
The cube root of 189 can be written as the product of the cube root of its prime factors. Therefore, the simplified cube root of 189 is:
cube root of 189 = cube root of (3 * 7)
= cube root of 3 * cube root of 7
= ∛3 * ∛7
= 3∛7
Therefore, the simplified cube root of 189 is 3∛7.
To simplify the cube root of 189, we can use prime factorization.
Step 1: Prime factorization of 189:
189 can be broken down into its prime factors as follows:
189 = 3 * 3 * 3 * 7
Step 2: Grouping the prime factors into triples:
Since we are looking for the cube root, we can arrange the prime factors into groups of three:
189 = (3 * 3) * (3 * 7)
Step 3: Simplifying the cube root:
The cube root of 3 * 3 is 3, and the cube root of 3 * 7 is ∛(3 * 7) = ∛21.
So, the simplified cube root of 189 is 3∛21.