Find the cubic root of 189.(1 point)
Responses
277–√3
27 root index 3 start root 7 end root
37–√
3 start root 7 end root
921−−√3
9 root index 3 start root 21 end root
37–√3
None of the given responses are correct.
To find the cubic root of 189, we need to find a number that, when multiplied by itself three times, equals 189.
By trial and error, we can find that the cubic root of 189 is approximately 5.849.
To find the cubic root of 189, we can simplify it further. The cubic root can be expressed as a power of 1/3.
37 – √3 (option) is not the correct answer since it represents a square root, not a cubic root.
27 root index 3 start root 7 end root is also not the correct answer since it represents the square root of 7, not the cubic root of 189.
921−−√3 (option) is also not the correct answer since it represents another square root.
The correct step-by-step process to find the cubic root of 189 is as follows:
1. Prime factorize the number 189: 189 = 3^3 × 7
2. Rewrite the number in terms of its prime factors:
189 = (3^3 × 7)^1/3
3. Simplify the expression:
189^(1/3) = (3^3 × 7)^1/3
4. Apply the exponent rules:
(3^3 × 7)^1/3 = 3^(3/3) × 7^(1/3)
5. Simplify the exponents:
3^(3/3) × 7^(1/3) = 3 × 7^(1/3)
So, the simplified expression for the cubic root of 189 is 3 × 7^(1/3).
To find the cubic root of 189, you need to find a number that, when multiplied by itself twice, equals 189. Let's go through the options provided and determine which one is correct.
Option 1: 277–√3
This is not the correct answer because the symbol "–√3" does not represent a valid mathematical operation.
Option 2: 27 root index 3 start root 7 end root
This option is also incorrect. The notation "root index 3 start root 7 end root" does not indicate the cubic root. The correct notation for the cubic root is ∛(cube root) or using the symbol √ placed above a smaller number (index).
Option 3: 921−−√3
This option is incorrect. The notation "−−√3" does not represent a valid mathematical operation.
Option 4: 37–√3
This is the correct answer. The cubic root of 189 is approximately 5.135 when rounded to three decimal places.