Find the cubic root of 189.(1 point)
Responses
37–√
3 start root 7 end root
277–√3
27 root index 3 start root 7 end root
37–√3
3 root index 3 start root 7 end root
921−−√3
3√7
To find the cubic root of 189, you can use a calculator or do it manually. Here is the correct answer:
The cubic root of 189 is approximately 5.848.
To find the cubic root of 189, you can either use a calculator or use prime factorization.
Using a calculator:
1. Enter 189.
2. Look for the button or function that calculates the cubic root on your calculator. It may be labeled as "∛" or "root 3".
3. Press the cubic root button/function and you will get the result.
Using prime factorization:
1. Break down 189 into its prime factors. Start by dividing it by the smallest prime number (2) and continue dividing by primes until you can no longer divide.
189 ÷ 3 = 63
63 ÷ 3 = 21
21 ÷ 3 = 7
2. The prime factorization of 189 is 3 * 3 * 7.
3. Since we want to find the cubic root, we need to find the perfect cube within the prime factorization. In this case, there is one group of 3's.
4. Take the number outside of the perfect cube (in this case, 3) and find its cubic root.
The cubic root of 3 is approximately 1.44.
5. Write down the result.
The cubic root of 189 is approximately 1.44 * ∛7 (or 1.44 * 7^(1/3)).
Therefore, the correct answer is 1.44 * ∛7.