find the square root of 96. 16√6 , 6√4 , 24 , 4√6
The square root of 96 is not exactly equal to any of the provided options. However, we can simplify it as follows:
The prime factorization of 96 is 2 * 2 * 2 * 2 * 2 * 3.
We can pair the factors of 2 to take them out of the square root:
√96 = √(2 * 2 * 2 * 2 * 2 * 3) = 2 * 2 * √(2 * 3) = 4√6.
Therefore, the simplified square root of 96 is 4√6.
To find the square root of 96, we can simplify it by factoring out perfect square factors. In this case, we can factor out 16, which is a perfect square.
√96 = √(16 * 6)
Next, we can separate the square root of 16 from the square root of 6.
= √16 * √6
= 4√6
Therefore, the square root of 96 is 4√6.
To find the square root of 96, we can use two methods: prime factorization and estimation.
Method 1: Prime Factorization
Step 1: Write down the prime factorization of 96.
96 = 2 * 2 * 2 * 2 * 2 * 3
Step 2: Pair the prime factors into groups of two.
96 = (2 * 2) * (2 * 2) * 3
Step 3: Simplify each pair into a single factor.
96 = 4 * 4 * 3
Step 4: Take the square root of the simplified expression.
√(96) = √(4 * 4 * 3)
= 4 * √(3)
= 4√3
Therefore, the square root of 96 is 4√3.
Method 2: Estimation
Since 96 lies between perfect squares, we can estimate the square root.
Step 1: Find the perfect squares on either side of 96.
9^2 = 81
10^2 = 100
Step 2: Choose the closer perfect square.
81 is closer to 96.
Step 3: Estimate the square root based on the chosen perfect square.
√(96) ≈ √(81)
≈ 9
Therefore, an approximation for the square root of 96 is 9.
Out of the options you provided, 4√6 is the closest to the actual square root of 96.
find the cubic root of 96
The cubic root of 96 can be found by finding a number when cubed gives us 96.
By prime factorizing 96, we get 2 * 2 * 2 * 2 * 2 * 3.
Grouping the factors in sets of three, we have (2 * 2 * 2) * (2 * 2 * 3).
Taking out the cubic root of each set, we get 2 * 2 * ∛(2 * 2 * 3).
Simplifying, we have 2 * 2 * ∛(12).
The cubic root of 12 is approximately 2.2894.
So, the cubic root of 96 is 2 * 2 * 2.2894 = 9.1576 (approx.).
find the cubic root of 96. 2^3√7 , 2^3√12 , 2√12 , 4√6
To find the cubic root of 96, we can simplify it using the prime factorization method.
Prime factorization of 96:
96 = 2 * 2 * 2 * 2 * 2 * 3
Now, let's group the factors in sets of three:
96 = (2 * 2 * 2) * (2 * 2 * 3)
Taking the cubic root of each group, we get:
(∛2 * ∛2 * ∛2) * (∛2 * ∛2 * ∛3)
Simplifying:
2 * 2 * ∛2 * ∛6
The simplified form of the cubic root of 96 is 4∛2∛6.
None of the options you provided match the simplified form.
didnt ask for simplest form
Apologies for the confusion.
The cubic root of 96, when not expressed in its simplest form, can be written as:
2^3√96 = 2^3√(2 * 2 * 2 * 2 * 2 * 3) = 2 * 2 * 2√(2 * 3) = 8√6.
Therefore, the cubic root of 96 can be expressed as 8√6.