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.
find the cubic root of 56, don't do simplest form
To find the cubic root of 56, we can use the prime factorization method.
The prime factorization of 56 is 2 * 2 * 2 * 7.
Now, let's group the factors in sets of three:
56 = (2 * 2 * 2) * 7
Taking the cubic root of each group, we get:
(∛2 * ∛2 * ∛2) * ∛7
Simplifying:
2 * 2 * ∛2 * ∛7
The cubic root of 56, without simplifying, can be expressed as 4∛2∛7.
find the cubic root of 32, don't do simplest form
To find the cubic root of 32, we can use the prime factorization method.
The prime factorization of 32 is 2 * 2 * 2 * 2 * 2.
Now, let's group the factors in sets of three:
32 = (2 * 2 * 2) * (2 * 2)
Taking the cubic root of each group, we get:
(∛2 * ∛2 * ∛2) * (∛2 * ∛2)
Simplifying:
2 * 2 * ∛2 * ∛2
The cubic root of 32, without simplifying, can be expressed as 4∛2∛2.
find the square root of 45
The square root of 45 is a non-repeating, non-terminating decimal number. However, we can approximate it using estimation:
Using estimation, we can find the perfect square that is closest to 45, which is 36 (since 6^2 = 36).
Since 45 is between 36 and 49, we can estimate the square root of 45 to be between 6 and 7.
We can further narrow down the estimate by taking the average of 6 and 7:
(6 + 7) / 2 = 6.5
Therefore, an approximate square root of 45 is 6.5.
square root of 175
The square root of 175 is an irrational number, which means it cannot be expressed as a finite decimal or a fraction. However, we can simplify it by breaking it down into prime factors and taking out perfect square factors.
The prime factorization of 175 is 5 * 5 * 7.
Since there are no pairs of identical factors, we cannot simplify this square root any further.
Thus, the square root of 175 is √175.
not simplfied
Apologies for the confusion. The square root of 175 can be simplified as follows:
The prime factorization of 175 is 5 * 5 * 7.
We can pair the factors of 5 to take them out of the square root:
√175 = √(5 * 5 * 7) = 5 * √7.
Therefore, the simplified square root of 175 is 5√7.
find the square of 200
The square of 200 is calculated by multiplying 200 by itself.
200^2 = 200 * 200 = 40,000.
Therefore, the square of 200 is 40,000.