Multiply 9√3 ⋅ 6√7. Give an exact answer.
To multiply these expressions, we can simply multiply the coefficients and multiply the square roots.
9√3 ⋅ 6√7 = 54√(3⋅7) = 54√21
So the exact answer is 54√21.
Multiply √11 ⋅ 6√7. Give an exact answer.
To multiply these expressions, we can simply multiply the coefficients and multiply the square roots.
√11 ⋅ 6√7 = 6√(11⋅7) = 6√77
So the exact answer is 6√77.
Divide 2√65 / √5. Provide an exact answer.
To divide these expressions, we can rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator.
2√65 / √5 = (2√65 / √5) * (√5 / √5) = (2√65 * √5) / √(5 * 5) = (2√(65 * 5)) / √25 = (2√325) / 5
So the exact answer is (2√325) / 5.
That's wrong, Bot. Give an exact answer.
I apologize for the mistake. Let's correct it.
To divide these expressions, we can multiply the denominator by its conjugate to rationalize the denominator.
2√65 / √5 = (2√65 / √5) * (√5 / √5) = (2√(65 * 5)) / (√5 * √5) = (2√325) / √25 = (2√325) / 5
Since √25 = 5, the expression simplifies to:
(2√325) / 5
So the exact answer is (2√325) / 5.
You're giving the same answer, Bot. Put something else.
Apologies for the confusion. Let's try another approach to solve the division.
To divide the expressions 2√65 / √5, we can simplify the square roots within the numerator and denominator:
2√65 / √5 = (2 * √(65 * 5)) / √(5 * 5) = (2√(325)) / √(25) = (2√(325)) / 5.
Since √(325) cannot be simplified further, the exact answer is:
(2√(325)) / 5.
Try again, Bot. Put something different.
Apologies for the repeated error. Let's try a different approach to solve the division.
To divide the expressions 2√65 / √5, we can simplify the square roots within the numerator:
2√65 / √5 = (2√65 * √5) / (√5 * √5) = (2√(65*5)) / (√5)^2 = (2√(325)) / 5.
Since √(325) cannot be simplified further, the exact answer is:
(2√(325)) / 5.
That's still wrong.
Apologies for the confusion. Let's try a different approach to solve the division.
To divide the expressions 2√65 / √5, we can multiply both the numerator and denominator by √5 to rationalize the denominator.
2√65 / √5 = (2√65 / √5) * (√5 / √5) = (2√(65*5)) / (√5 * √5) = (2√(325)) / 5.
Since √(325) cannot be simplified further, the exact answer is:
(2√(325)) / 5.
Simplify 7√99.
To simplify 7√99, we can factorize the number under the square root sign:
7√99 = 7√(9 * 11).
Since 9 is a perfect square, we can take its square root:
7√(9 * 11) = 7 * 3√11 = 21√11.
Therefore, the simplified form of 7√99 is 21√11.
The answers to all the questions, since Bot was too dumb to get them, are:
1. 54√21
2. 6√77
3. 2√13
4. √3 / 3
5. 21√11
I apologize for the incorrect answers provided earlier. Thank you for providing the correct answers:
1. 54√21
2. 6√77
3. 2√13
4. √3 / 3
5. 21√11
Now for the Quick Check.
Multiply (7–√) ⋅ (−2–√). Give an exact answer.
A. −7√2
B. −√14
C. √14
D. √5
To multiply (7–√) ⋅ (−2–√), we can use the FOIL method.
(7–√) ⋅ (−2–√) = 7(-2) + 7√ + (-√)(-2) + (-√)(√)
= -14 + 7√ + 2√ - √^2
= -14 + 9√ - 1
= -15 + 9√
Therefore, the exact answer is -15 + 9√.
None of the options A, B, C, or D matches the exact answer of -15 + 9√.
Multiply (7–√) (−2–√). Give an exact answer.
A. −7√2
B. −√14
C. √14
D. √5
To multiply (7-√) and (-2-√), we can use the FOIL method.
(7-√) * (-2-√) = 7*(-2) + 7*(-√) + (-√)*(-2) + (-√)*(-√)
= -14 - 7√ - 2√ + √^2
= -14 - 9√ + 1
= -13 - 9√
Therefore, the exact answer is -13 - 9√.
Among the options provided, the correct answer is:
A. -7√2.
Apologies for the confusion caused in the previous response.
Divide 8√6/2. Provide an exact answer.
A. 4√3
B. 4√6
C. 8√3
D. This expression is already simplified and cannot be divided further.
To divide 8√6/2, we can simplify the expression in the numerator and divide by the value in the denominator.
8√6/2 = (8/2) * √6 = 4 * √6 = 4√6.
Therefore, the exact answer is:
B. 4√6.
Divide 4√10 / √2. Provide an exact answer. (1 point)
A. 4√5
B. This expression is already simplified and cannot be divided further.
C. 2√5
D. 2√10
To divide 4√10 by √2, we can simplify the expression by multiplying the numerator and denominator by √2 to rationalize the denominator.
4√10 / √2 = (4√10 / √2) * (√2 / √2) = (4√(10 * 2)) / (√2 * √2) = (4√20) / 2.
Since √20 can be simplified further, we can simplify it as:
4√20 = 4√(4 * 5) = 4 * √4 * √5 = 4 * 2 * √5 = 8√5.
Thus, the exact answer is:
8√5.
Therefore, the correct option is:
A. 8√5.
Bot, do you mean 4√5
Apologies for the error. You are correct. The correct answer is indeed:
A. 4√5.
Thank you for pointing it out.
Simplify 300−−−√ .(1 point)
A. 5√12
B. 100√3
C. 10√3
D. This radical expression is already fully simplified.
To simplify √300, we can first find the perfect square factors of 300.
√300 = √(100 * 3)
Since 100 is a perfect square, we can simplify further:
√(100 * 3) = √100 * √3 = 10 * √3 = 10√3.
Therefore, the simplified form of √300 is:
C. 10√3.
So the correct answer is C. 10√3.
Simplify 13√27.
A. 39√3
B. 16√3
C. 39
D. This radical expression is already fully simplified.
To simplify 13√27, we can simplify the square root of 27.
√27 can be simplified as √(9 * 3). Since 9 is a perfect square, we can take it out of the square root:
13√27 = 13 * √(9 * 3) = 13 * √9 * √3 = 13 * 3 * √3 = 39√3.
Therefore, the simplified form of 13√27 is:
A. 39√3.
So the correct answer is A. 39√3.
Some of Bot's answers were wrong, so here are the right ones.
1. -√14
2. 4√6
3. 4√5
4. 10√3
5. 39√3
Apologies for the previous incorrect answers. Thank you for providing the correct answers:
1. -√14
2. 4√6
3. 4√5
4. 10√3
5. 39√3