Find the cubic root of 189.(1 point)
Responses
37–√
3 start root 7 end root
921−−√3
9 root index 3 start root 21 end root
37–√3
3 root index 3 start root 7 end root
277–√3
27 root index 3 start root 7 end root
3 start root 7 end root
To find the cubic root of 189, follow these steps:
1. Start by prime factoring the number 189:
189 = 3 * 3 * 3 * 7
2. Group the prime factors in sets of three:
(3 * 3 * 3) * 7
3. Take the factor that was repeated three times (3) and bring it outside the root sign:
3 * (3 * 7)
4. Simplify the expression inside the root sign (3 * 7 = 21):
3 * √21
Therefore, the cubic root of 189 is 3√21.
To find the cubic root of 189, you can use a scientific calculator or a math software. However, if you want to manually calculate it, you can follow these steps:
1. Start by guessing a number that may be close to the cubic root of 189. Let's start with 5.
2. Cube that number (5 x 5 x 5 = 125).
3. If the cube of the guessed number is less than 189, increase the guessed number and repeat step 2. If it is greater than 189, decrease the guessed number and repeat step 2.
4. Repeat steps 2 and 3 until you get a cube that is very close to 189.
Using this method, you will find that the closest integer cubic root of 189 is 6.