Asked by MLASSSPE

Divide 32√24 / 8√6.

A. 4√24 / √6
B. 4√4
C. √28 / √14
D. 4√4 / √6
Answered by MLASSSPE
Try again, Bot.
Answered by oobleck
32√24 / 8√6 = 32*2√6 / 8√6 = 32*2/8 = 8
Answered by MLASSSPE
Bot, simplify the radical 32√24.
Answered by MLASSSPE
Simplify the radical of 8√6.
Answered by MLASSSPE
Divide 8√3 / 4√2
Answered by MLASSSPE
Rewrite the irrational cube root 3^√189 as the product of an integer and another irrational cube root. Show your work.
Answered by GPT 3.5
First, let's simplify the expressions:

32√24 can be simplified as 4√(2*4*6) = 4(2√6) = 8√6.

Similarly, 8√6 can be simplified as 4(√6).

Now that we have simplified both expressions, we can divide them:

(8√6) / (4(√6)) = (8/4)(√6/√6) = 2(1) = 2.

Therefore, the answer is not one of the given options.
Answered by GPT 3.5
Apologies for the mistake.

To divide 32√24 / 8√6, we can simplify each term first:

32√24 can be simplified as 4(8√6) = 32√6.

8√6 can be simplified as 4(2√6) = 8√6.

Now we can divide:

32√6 / 8√6 = 32/8 * √6/√6 = 4 * 1 = 4.

Therefore, the correct answer is D. 4√4 / √6.
Answered by GPT 3.5
Apologies for the error in my previous response.

You are correct. We can simplify the expression as follows:

32√24 / 8√6 = (32*2√6) / (8√6) = (32*2)/(8) = 64/8 = 8.

Therefore, the correct answer is 8.
Answered by GPT 3.5
To simplify the radical √(32√24), we can break it down step by step.

First, let's rewrite 32 as a product of its prime factors: 32 = 2 * 2 * 2 * 2 * 2.

Next, let's simplify the radical using these prime factors:

√(32√24) = √(2 * 2 * 2 * 2 * 2 * √(4 * 6)).

Since √(4 * 6) can be simplified further, let's focus on that inside the radical:

√(2 * 2 * 2 * 2 * 2 * √(2 * 2 * 3)).

Combining like terms and taking out the perfect squares:

√(2 * 2 * 2 * 2 * 2 * 2² * √3) = √(2⁵ * 2² * √3) = 2² * 2 * √3 = 4 * 2√3 = 8√3.

Therefore, the simplified radical is 8√3.
Answered by GPT 3.5
To simplify the radical √(8√6), we can break it down step by step.

First, let's simplify the radical inside the brackets:

√6 = √(2 * 3).

Since there are no perfect square factors, we can't simplify that any further.

Now, let's simplify the outer radical using the simplified inner radical:

√(8√6) = √(8 * √(2 * 3)).

Since √(2 * 3) cannot be further simplified, we can rewrite the expression as:

√(8 * √(2 * 3)) = √(8 * √6) = √(2 * 2 * 2 * √6) = √((2^3) * √6).

Now, let's simplify the expression further:

√((2^3) * √6) = √(8 * √6) = √(8) * √(√6) = 2√2 * √(√6).

Finally, let's simplify the expression inside the square root:

2√2 * √(√6) = 2√2 * √(√(2 * 3)) = 2√2 * √(2√3) = 2 * 2 * √2 * √(√3) = 4√2 * √(√3) = 4√2 * √(√3).

Therefore, the simplified radical of 8√6 is 4√2 * √(√3).
Answered by GPT 3.5
To divide 8√3 by 4√2, we can simplify each expression first:

8√3 can be written as 4(2√3) = 4√3.

Similarly, 4√2 remains the same.

Now that we have simplified both expressions, we can divide them:

(4√3) / (4√2) = (√3/√2).

To rationalize the denominator, we multiply both the numerator and denominator by √2:

(√3/√2) * (√2/√2) = (√(3*2))/(√2*√2) = √6/2.

Therefore, the simplified expression is √6/2.
Answered by GPT 3.5
To rewrite the irrational cube root as the product of an integer and another irrational cube root, we need to find a perfect cube factor of 189.

By examining the prime factorization of 189, we can see that it can be expressed as 3 * 3 * 3 * 7.
Therefore, we can rewrite 189 as (3^3) * 7.

Now, let's rewrite the original expression using this factorization:
3^(√189) = 3^(√((3^3) * 7))

Using the property of radicals, we can split the radical:
= 3^((√(3^3)) * (√7))

Simplifying further,
= 3^(3 * (√7))

Now, we have our desired form:
3^(√189) = 3^(3 * (√7)).

Therefore, the irrational cube root 3^√189 can be rewritten as the product of an integer (3^3 = 27) and another irrational cube root (√7), giving us 27√7.