Find the cubic root of 96.(1 point) Responses 27–√3 2 root index 3 start root 7 end root 212−−√3 2 root index 3 start root 12 end root 212−−√ 2 start root 12 end root 46–√
To find the cubic root of 96, we need to find a number that, when multiplied by itself three times, equals 96.
Let's start by taking the prime factorization of 96: 96 = 2^5•3.
Next, we need to group the factors in sets of three, since we are looking for the cubic root. We have one set of three 2s and one set of three 2s and one 3 that are left over.
Taking one 2 and one 3 out of the cube root, we are left with 2^2•3 = 12.
Therefore, the cubic root of 96 is 2∛12.
To find the cubic root of 96, follow these steps:
Step 1: Start by prime factorizing the number 96.
96 = 2^5 × 3
Step 2: Group the prime factors into triples, as each group represents one factor of the cubic root.
96 = (2^3 × 3) × (2^2)
Step 3: Take the cubic root of each triple.
(2^3 × 3) = 2 × 1 = 2
(2^2) = 2
Step 4: Combine the results to find the final answer.
Cubic root of 96 = 2 × 2 = 4
Therefore, the cubic root of 96 is 4.
To find the cubic root of 96, we need to find the number that, when multiplied by itself three times, equals 96. Let's break down the steps to solve it:
1. Start by guessing a number that could potentially be close to the cubic root of 96. Let's choose 4.
2. Cube the guessed number: 4 * 4 * 4 = 64.
3. Compare the result with 96.
- Since 64 is smaller than 96, we need to increase our guess. Let's try 5.
4. Cube the new guess: 5 * 5 * 5 = 125.
5. Compare the result (125) with 96.
- Since 125 is greater than 96, we now know that the cubic root of 96 is less than 5.
6. Continue narrowing down the range by guessing numbers between 4 and 5. A good next guess is the midpoint between the two: (4 + 5) / 2 = 4.5.
7. Cube the new guess: 4.5 * 4.5 * 4.5 = 91.125.
8. Compare the result (91.125) with 96.
- Since 91.125 is smaller than 96, we now know that the cubic root of 96 is greater than 4.5.
9. Repeat steps 6-8 with a new guessed number between 4.5 and 5. A good next guess is the midpoint: (4.5 + 5) / 2 = 4.75.
10. Cube the new guess: 4.75 * 4.75 * 4.75 = 95.847.
11. Compare the result (95.847) with 96.
- Since 95.847 is smaller than 96, we now know that the cubic root of 96 is greater than 4.75.
12. Keep repeating steps 6-8 with smaller and smaller intervals until you reach an accurate enough result. The more precise you want the result to be, the more iterations you will need to do.
Based on this iterative process, we can conclude that the cubic root of 96 is approximately 4.756.