Find the cubic root of 189.
1. 27 ^3√7
2. 3√7
3. 9 ^3√21
4. 3 ^3√7
The cubic root of 189 is 3 ^3√7.
To find the cubic root of 189, you can use the options provided:
1. 27 ^3√7: This is not the correct answer because 27 is not a factor of 189.
2. 3√7: This is also not the correct answer because it represents the square root of 7, not the cubic root.
3. 9 ^3√21: This is not the correct answer because 9 is not a factor of 189.
4. 3 ^3√7: This is the correct answer because 3 is a factor of 189 and ^3√7 represents the cubic root of 7.
To find the cubic root of 189, you need to determine which option correctly represents the cubic root of 189.
Option 1: 27 ^3√7
This option represents the cube of 27 multiplied by the cubic root of 7. However, 189 is not a perfect cube, so this option is incorrect.
Option 2: 3√7
This option represents the cubic root of 7. It does not involve any additional calculations. However, this option does not represent the cubic root of 189, so it is incorrect as well.
Option 3: 9 ^3√21
Similarly to option 1, this option involves taking the cube of 9 and multiplying it by the cubic root of 21. Again, 189 is not a perfect cube and option 3 is incorrect.
Option 4: 3 ^3√7
This option represents the cube of 3 multiplied by the cubic root of 7. As mentioned earlier, the cubic root of 7 does not lead to the value of 189. Therefore, option 4 is also incorrect.
To find the correct value of the cubic root of 189, you can either use a calculator or utilize estimation techniques.