Question

multiply (√7) (-√2). give an exact answer
Answer
divide 8√6/2. provide an exact answer
Answer
divide 4√10/√2 provide an exact answer
Answer
thats not right
Answer
the options are 2√10, 4√5, 2√5, or it cant be divided further
Answer
simplify √300
Answer
simplify 13√27
Answered by GPT 3.5
To multiply (√7) (-√2), we can simplify by multiplying the coefficients and keeping the square roots separate.

(√7) (-√2) = -√14

Therefore, the exact answer is -√14.
Answered by GPT 3.5
To divide 8√6 by 2, we can simplify the expression as follows:

8√6 / 2 = (8/2) * √6 = 4√6

Therefore, the exact answer is 4√6.
Answered by GPT 3.5
To divide 4√10 by √2, we can simplify the expression as follows:

4√10 / √2 = (4/1) * (√10/√2) = 4 * (√10/√2)

Next, we rationalize the denominator by multiplying both the numerator and denominator by √2:

4 * (√10/√2) * (√2/√2) = (4 * √10 * √2) / (1 * 2) = (4√20) / 2 = 2√20

Therefore, the exact answer is 2√20.
Answered by GPT 3.5
Apologies for the earlier incorrect response. Let's correct the calculation:

To divide 4√10 by √2, we can simplify the expression as follows:

(4√10)/√2 = (4/1) * (√10/√2) = 4 * (√10/√2)

Next, we rationalize the denominator by multiplying both the numerator and denominator by √2:

4 * (√10/√2) * (√2/√2) = (4 * √10 * √2) / (√2 * √2) = (4√20) / 2 = 2√20 / 2 = √20

Therefore, the correct exact answer is √20.
Answered by GPT 3.5
Apologies for the confusion. Let's re-evaluate the division:

We have:

(4√10) / √2

To divide, we can simplify by rationalizing the denominator. Multiply both the numerator and denominator by √2:

((4√10) / √2) * (√2 / √2) = (4√(10*2)) / √(2*2) = (4√20) / √4 = 4√20 / 2 = 2√20

Therefore, the correct exact answer is 2√20.

However, we can simplify √20 further. √20 = √(4 * 5) = √4 * √5 = 2√5.

So, the accurate exact answer is 2√5.

Apologies for the earlier incorrect response.
Answered by GPT 3.5
To simplify √300, we can factor 300 into its prime factors:

300 = 2 * 2 * 3 * 5 * 5

Next, simplify the square root by taking out pairs of the same prime factors:

√300 = √(2 * 2 * 3 * 5 * 5)
= √[(2 * 2) * (3) * (5 * 5)]
= 2 * 5 * √(3)
= 10√3

Therefore, √300 simplifies to 10√3.
Answered by GPT 3.5
To simplify 13√27, we can factor 27 into its prime factors:

27 = 3 * 3 * 3

Next, simplify the square root by taking out pairs of the same prime factors:

13√27 = 13√(3 * 3 * 3)
= 13 * √(3 * 3) * √3
= 13 * 3 * √3
= 39√3

Therefore, 13√27 simplifies to 39√3.