Multiply (square root7)x(−square root2) . Give an exact answer.
To multiply square roots, you can multiply the numbers under the square roots together and keep the square root of the product.
The product of (square root of 7) and (-square root of 2) is:
√7 * (- √2)
√(7 * 2) * (-1) (Multiplying the numbers under the square roots together)
√14 * (-1)
The exact answer is -√14.
Divide 8square root6 /2 . Provide an exact answer.(1 point)
Responses
43–√
4 start root 3 end root
46–√
4 start root 6 end root
This expression is already simplified and cannot be divided further.
This expression is already simplified and cannot be divided further.
83–√
To divide by a number outside of the square root, you can divide each term inside the square root individually by that number.
Given the expression 8√6 / 2, we can divide both the coefficient (8) and the term inside the square root (√6) individually by 2.
8 / 2 = 4
√6 / 2 = √(6/2) = √3
So, the exact answer is 4√3.
Divide 4square root10/square root2 . Provide an exact answer. (1 point)
Responses
45–√
4 start root 5 end root
This expression is already simplified and cannot be divided further.
This expression is already simplified and cannot be divided further.
210−−√
2 start root 10 end root
25–√
To divide square roots, you can divide the numbers inside the square roots while keeping the square root symbol.
Given the expression (4√10) / √2, we can divide the numbers inside the square roots:
√10 / √2 = √(10/2) = √5
So, the exact answer is 4√5.
Simplify square root300.(1 point)
Responses
This radical expression is already fully simplified.
This radical expression is already fully simplified.
512−−√
5 start root 12 end root
103–√
10 start root 3 end root
1003–√
We can simplify the square root of 300 by factoring it into perfect squares.
First, we factor 300:
300 = 100 * 3
Then, we can simplify the square root by taking the square root of each perfect square factor:
√300 = √(100 * 3) = √100 * √3 = 10√3
So, the simplified form is 10√3.
Simplify 13square root27 .(1 point)
Responses
This radical expression is already fully simplified.
This radical expression is already fully simplified.
39
39
393–√
39 start root 3 end root
163–√
To simplify the expression 13√27, we can factor the number 27 into perfect squares.
27 can be factored as 3 * 3 * 3, which means it has a perfect square factor of 3.
We can simplify the expression by taking out the perfect square factor outside the square root:
13√27 = 13√(3 * 3 * 3) = 13 * 3√3 = 39√3
Therefore, the simplified form of 13√27 is 39√3.
Can you recheck all your answers?
Apologies for any confusion. Let's recheck the answers.
1. Multiply (square root of 7) and (-square root of 2):
The product is -√14.
2. Divide 8√6 by 2:
The simplified form is 4√6.
3. Divide 4√10 by √2:
The simplified form is 2√5.
4. Simplify √300:
The simplified form is 10√3.
5. Simplify 13√27:
The simplified form is 39√3.
Thank you for bringing this to my attention, and I apologize for any confusion caused.
so your saying 2. and 3. is wrong?
Apologies for the incorrect responses. Let's correct them:
2. Divide 8√6 by 2:
The simplified form is 4√6.
3. Divide 4√10 by √2:
To divide square roots, we rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator (√2).
(4√10) / (√2) = (4√10 * √2) / (√2 * √2)
= (4√(10 * 2)) / (√(2 * 2))
= (4√20) / (√4)
= (4√20) / 2
= 2√20
= 2√(4 * 5)
= 2√4 * √5
= 2 * 2√5
= 4√5
So, the correct answer for 4√10 / √2 is 4√5.
I apologize for the confusion caused by the previous incorrect responses. Please let me know if you have any further questions or if there's anything else I can assist you with.
1. -square root14 Correct
2. 4square root6 Correct
3. 4square root5 Correct
4. 10square root3 Correct
5. 39square root3 Correct
Thank you bot you give me a 100%.