Find the cubic root of 189.
O 9√21
O 27√7
O 3√7
O 3√7
The cubic root of 189 is approximately 5.568. None of the answer options provided match this result.
To find the cubic root of 189, you can follow these steps:
Step 1: Prime factorize the number 189.
189 = 3 * 3 * 3 * 7
Step 2: Rewrite 189 using its prime factorization.
189 = 3^3 * 7
Step 3: Take the cubic root of each factor.
3√(3^3 * 7)
Step 4: Simplify.
3 * √(7)
Therefore, the cubic root of 189 is 3√7.
To find the cubic root of 189, you can calculate it by using a calculator or by breaking down the number into its prime factorization and simplifying.
To do it manually, start by finding the prime factors of 189. Divide 189 by the smallest prime number, which is 3, and you get 63. Divide 63 by 3 again, and you get 21. Finally, dividing 21 by 3 gives you 7.
So the prime factorization of 189 is 3 x 3 x 3 x 7.
Now, to find the cubic root, we need to group the prime factors into threes. In this case, we have three 3's and one 7.
Taking one 3 and one 7 out, we have (3 x 3 x 7)^(1/3) = (9 x 7)^(1/3) = 63^(1/3).
Simplifying further, we have the cubic root of 63.
Now, we can approximate the cube root of 63 using a calculator, which is approximately 3.981071706.
So, the correct answer for the cubic root of 189 is:
O 3√7.