Find the cubic root of 189. (1 point)
O 27 * root(7, 3)
O 3 * root(7, 3)
9 * root(21, 3)
3sqrt(7)
The cubic root of 189 is 3 * ∛(7).
To find the cubic root of 189, we need to find a number that, when multiplied by itself three times, equals 189.
Here is how we can find the answer:
1. Start by factoring 189 into its prime factors.
The prime factorization of 189 is 3 * 3 * 3 * 7.
2. Group the prime factors into sets of three, since we are looking for the cubic root.
We have one set of three 3's and one set of three 7's.
3. Take one number from each set.
From the set of three 3's, we take one 3. From the set of three 7's, we take one 7.
4. Multiply the numbers we have taken.
3 * 7 = 21.
So, the cubic root of 189 is 21.
Therefore, the correct answer is 9 * root(21, 3).
To find the cubic root of 189, follow these steps:
Step 1: Prime factorize 189
The prime factors of 189 are: 3, 3, 3, and 7
Step 2: Group the prime factors into groups of three, since we are finding the cubic root:
(3 * 3 * 3) * 7
Step 3: Simplify each group of three:
(3 * 3 * 3) = 27
Step 4: Write the simplified expression:
27 * sqrt(7)
So, the cubic root of 189 is represented as 27 * sqrt(7).