Find the cubic root of 189.
O 9√21
O 27√7
O 3√7
O 3√7
which one is right?
The correct answer is O 3√7
To find the cubic root of 189, we need to find a number that, when multiplied by itself three times, equals 189.
Let's check the options given:
Option A: 9√21
Option B: 27√7
Option C: 3√7
Option D: 3√7
To determine the correct option, we can simplify each option and check if it equals 189 when raised to the power of 3.
Let's simplify each option:
Option A: 9√21 = 9 * √(21) = 9 * √(3 * 7) = 9 * √3 * √7 = 9√3√7
Option B: 27√7 = 27 * √7
Option C: 3√7 = 3 * √7
Option D: 3√7
None of the options can be simplified further, so let's check if any of them equals 189 when raised to the power of 3:
Option A: (9√3√7)^3 = (9*3)*(√3*√3)*(√7*√7) = 27*(3)*(7) = 567 ≠ 189
Option B: (27√7)^3 = (27)*(√7)*(√7)*(√7) = 27*(7)*(7)*(√7) = 1323√7 ≠ 189
Option C: (3√7)^3 = (3)*(√7)*(√7)*(√7) = 3*(7)*(7)*(√7) = 147√7 ≠ 189
Option D: (3√7)^3 = (3)*(√7)*(√7)*(√7) = 3*(7)*(7)*(√7) = 147√7 ≠ 189
None of the options equals 189 when raised to the power of 3. Therefore, none of the given options is correct.
To find the cubic root of 189, you can use a scientific calculator or perform long division manually. However, let's go through the steps of performing long division to find the answer.
1. Start by guessing the cube root of 189. Since the cube root should be between 5 and 6, let's start with 5 as a guess.
Trial Division:
- 5
------------
5 | 189
2. Multiply the guess (5) by itself twice to get 125.
- 5
------------
5 | 189
125
3. Divide 189 by the square of the guess (125) and write the result (0) above the line.
- 5
------------
5 | 189
125
0
4. To get the next digit of the answer, bring down the next two digits from the original number, which is 89.
- 5
------------
5 | 189
125
---
89
5. Double the previous quotient (0) and add a digit to get a new guess. In this case, the new guess is 10.
- 5
------------
5 | 189
125
---
89
85
6. Multiply the entire divisor (55) by the new guess (10) to get the new dividend (550).
- 5
------------
5 | 189
125
---
89
85
-----
550
7. Repeat steps 3-6 for the new dividend (550).
- 5 10
------------
5 | 189
125
---
89
85
-----
550
- 5 10
------------
5 | 189
125
---
89
85
-----
550
550
8. Continue this process until you have enough decimal places or have reached the desired degree of accuracy.
By following these steps, you will find that the correct answer for the cubic root of 189 is 5.890.
Based on the options provided, it seems there might be an error. None of the given options match the correct answer calculated through the division process.