Find the cubic root of 189.(1 point) Responses 37–√3 3 root index 3 start root 7 end root 921−−√3 9 root index 3 start root 21 end root 277–√3 27 root index 3 start root 7 end root 37–√
The correct response is 3 root index 3.
To find the cubic root of 189, you can use a calculator or the method of prime factorization. Here's how you can use the method of prime factorization:
1. Start by finding the prime factorization of 189:
189 = 3 * 3 * 7
2. Group the prime factors in sets of three:
(3 * 3) * 7 = 27 * 7
3. Take the cubic root of each group of three:
∛27 = 3
∛7 = ∛7
4. Combine the results:
3 * ∛7
So, 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 twice, gives us 189.
One way to find the cubic root is to use the prime factorization of 189.
First, let's find the prime factors of 189:
189 = 3^3 × 7^1
Now, we can try to group the prime factors into sets of three. In this case, we have one group of three 3s and one group of one 7.
Taking one factor from each group, we get:
3 × 7 = 21
So, the cubic root of 189 is 21.
In the given responses, the correct answer is "9 root index 3 start root 21 end root".