Find the cubic root of 189. (1 point)
0 3sqrt(7)
© 9 * root(21, 3)
© 27 * root(7, 3)
© 3 * root(7, 2)
The cubic root of 189 is 3 * root(7, 2).
To find the cubic root of 189, we need to find the number that, when multiplied by itself three times, gives us 189. Let's check the options given:
1) 0: The cubic root of 0 is 0, but 0 is not equal to 189.
2) 3sqrt(7): This is the square root of 7 multiplied by 3. Cubing this value will give a different result than 189.
3) 9 * root(21, 3): This option includes the 3rd root of 21. However, we need to find the cubic root of 189, not 21.
4) 27 * root(7, 3): This option includes the cubic root of 7. If we cube this value (27*7 = 189), it matches the desired result. Therefore, the correct cubic root of 189 is 27 * root(7, 3).
So, the correct answer is © 27 * root(7, 3).
To find the cubic root of 189, we need to find a number that, when cubed, gives us 189. Here's one way to solve it:
1. Start by prime factorizing 189: 189 = 3 * 3 * 3 * 7.
2. Since we're looking for the cubic root, we need to group the factors in sets of three. In this case, we have three 3s and one 7.
3. Take one factor from each group of three and combine them. For the 3s, we take one 3 and for the 7, we take the whole factor since it has no other factors to group it with.
4. Calculate the cubic root of the combined factors: cubic root of (3 * 3 * 3 * 7) = 3 * cubic root of 7.
5. Simplify the expression: cubic root of 189 = 3 * cubic root of 7.
Therefore, the correct answer is © 3 * root(7, 2).