Find the cubic root of 135.(1 point)
Responses
35–√
3 start root 5 end root
5–√3
root index 3 start root 5 end root
35–√3
3 root index 3 start root 5 end root
527−−√3
5 root index 3 start root 27 end root
The correct response is:
3√135
out of the responses
The correct response is: 3√135
To find the cubic root of 135, we need to find a number that, when multiplied by itself three times, gives us 135. Let's break down the steps to find the answer.
Step 1: Prime Factorization
First, we need to find the prime factorization of 135. We can do this by factoring it into its prime factors. 135 can be written as 3 x 3 x 3 x 5, or 3^3 x 5.
Step 2: Grouping Factors
Next, we can group the factors in sets of three, as we're looking for the cubic root. In this case, we can take one 3 from the factorization as a group and leave the other two 3s and the 5 as a separate group. So, the groups are (3)^1 x (3^2 x 5).
Step 3: Taking the Cubic Root
Next, we can take the cubic root of each group. In the first group, we have (3)^1, which equals 3. In the second group, we have (3^2 x 5), which equals 9 x 5 = 45.
Step 4: Combine Results
Finally, we can combine the results from step 3 to find the final answer. The cubic root of 135 is 3 x 45 = 135.
So, the correct answer is 3√45 (or root 45 with index 3).