Multiply (−8√21)(−7√2) . Give an exact answer.(1 point)
Responses
−√42
negative start root 42 end root
56√19
56 start root 19 end root
−56√42
negative 56 start root 42 end root
56√42
33 answers
The answer is -56√42.
Incorrect
Apologies for the incorrect response. Let's go through the steps again:
Step 1: Multiply the coefficients (-8 and -7): -8 * -7 = 56.
Step 2: Multiply the radicals (√21 and √2): √21 * √2 = √(21 * 2) = √42.
Step 3: Combine the result from step 1 with the result from step 2: 56 * √42.
Therefore, the correct answer is: 56√42.
Step 1: Multiply the coefficients (-8 and -7): -8 * -7 = 56.
Step 2: Multiply the radicals (√21 and √2): √21 * √2 = √(21 * 2) = √42.
Step 3: Combine the result from step 1 with the result from step 2: 56 * √42.
Therefore, the correct answer is: 56√42.
Multiply (-3√6) (√5). Give an exact answer.
Responses
√90
3√30
-3√30
3√11
Responses
√90
3√30
-3√30
3√11
To multiply (-3√6) and (√5), you can follow these steps:
Step 1: Multiply the coefficients (-3 and 1): -3 * 1 = -3.
Step 2: Multiply the radicals (√6 and √5): √6 * √5 = √(6 * 5) = √30.
Step 3: Combine the result from step 1 with the result from step 2: -3√30.
Therefore, the exact answer to the multiplication (-3√6)(√5) is -3√30.
Step 1: Multiply the coefficients (-3 and 1): -3 * 1 = -3.
Step 2: Multiply the radicals (√6 and √5): √6 * √5 = √(6 * 5) = √30.
Step 3: Combine the result from step 1 with the result from step 2: -3√30.
Therefore, the exact answer to the multiplication (-3√6)(√5) is -3√30.
Its 3 √ 30
Apologies for the mistake again. You are correct. Let's go through the steps one more time:
Step 1: Multiply the coefficients (-3 and 1): -3 * 1 = -3.
Step 2: Multiply the radicals (√6 and √5): √6 * √5 = √(6 * 5) = √30.
Step 3: Combine the result from step 1 with the result from step 2: -3√30.
Therefore, the correct answer is -3√30. Thank you for pointing out the mistake.
Step 1: Multiply the coefficients (-3 and 1): -3 * 1 = -3.
Step 2: Multiply the radicals (√6 and √5): √6 * √5 = √(6 * 5) = √30.
Step 3: Combine the result from step 1 with the result from step 2: -3√30.
Therefore, the correct answer is -3√30. Thank you for pointing out the mistake.
Divide 12√15/3. Provide an exact answer.
Responses
4√5
This expression is already simplified and cannot be divided further.
4√15
12√5
Responses
4√5
This expression is already simplified and cannot be divided further.
4√15
12√5
To divide 12√15 by 3, you can divide the coefficient (12) by the divisor (3) and keep the same radical (√15).
12 ÷ 3 = 4
Therefore, the exact answer is 4√15.
12 ÷ 3 = 4
Therefore, the exact answer is 4√15.
Simplify 3√56
To simplify √56, we can find the largest perfect square that divides evenly into 56.
The largest perfect square that divides evenly into 56 is 4, which is the square of 2.
√56 can be written as √(4 * 14).
We can then simplify this further as 2√14.
Therefore, the simplified form of 3√56 is 3 * 2√14, which is equal to 6√14.
The largest perfect square that divides evenly into 56 is 4, which is the square of 2.
√56 can be written as √(4 * 14).
We can then simplify this further as 2√14.
Therefore, the simplified form of 3√56 is 3 * 2√14, which is equal to 6√14.
What is the irrational square root √72 rewritten as the product of an integer and another irrational square root?(1 point)
Responses
6 √ 2
6 start root 2 end root
36 √ 2
36 start root 2 end root
3 √ 8
3 start root 8 end root
2 √ 18
Responses
6 √ 2
6 start root 2 end root
36 √ 2
36 start root 2 end root
3 √ 8
3 start root 8 end root
2 √ 18
To rewrite the irrational square root √72 as the product of an integer and another irrational square root, we can first identify the largest perfect square that divides evenly into 72. In this case, it is 36.
√72 can be rewritten as √(36 * 2).
We can then simplify this further as 6√2.
Therefore, the rewritten form of √72 is 6√2.
√72 can be rewritten as √(36 * 2).
We can then simplify this further as 6√2.
Therefore, the rewritten form of √72 is 6√2.
What is √54 simplified
Responses
69–√
6 start root 9 end root
227−−√
2 start root 27 end root
36–√
3 start root 6 end root
272
Responses
69–√
6 start root 9 end root
227−−√
2 start root 27 end root
36–√
3 start root 6 end root
272
To simplify √54, we can find the largest perfect square that divides evenly into 54.
The largest perfect square that divides evenly into 54 is 9, which is the square of 3.
√54 can be written as √(9 * 6).
We can then simplify this further as 3√6.
Therefore, the simplified form of √54 is 3√6.
The largest perfect square that divides evenly into 54 is 9, which is the square of 3.
√54 can be written as √(9 * 6).
We can then simplify this further as 3√6.
Therefore, the simplified form of √54 is 3√6.
69–√
6 start root 9 end root
227−−√
2 start root 27 end root
36–√
3 start root 6 end root
272
6 start root 9 end root
227−−√
2 start root 27 end root
36–√
3 start root 6 end root
272
Apologies for the confusion. The correct simplified form of √54 is 3√6, as previously stated.
Therefore, the correct response is:
3 start root 6 end root.
Therefore, the correct response is:
3 start root 6 end root.
What is the irrational cube root −16−−−−√3 rewritten as a product of an integer and another irrational cube root?(1 point)
Responses
−4
negative 4
42–√3
4 root index 3 start root 2 end root
22–√3
2 root index 3 start root 2 end root
−22–√3
Responses
−4
negative 4
42–√3
4 root index 3 start root 2 end root
22–√3
2 root index 3 start root 2 end root
−22–√3
To rewrite the irrational cube root −16√3 as a product of an integer and another irrational cube root, we can begin by factoring the cube root.
The cube root of -16 is -2, and the cube root of 3 remains as √3.
Therefore, the rewritten form is -2√3.
Therefore, the correct response is:
−2 root index 3 start root 3 end root.
The cube root of -16 is -2, and the cube root of 3 remains as √3.
Therefore, the rewritten form is -2√3.
Therefore, the correct response is:
−2 root index 3 start root 3 end root.
The answer is -2 3 √2
Apologies for the confusion. Let's go through the steps to rewrite the irrational cube root -16√3 as a product of an integer and another irrational cube root:
The cube root of -16 is -2 because (-2)^3 = -16.
The cube root of 3 is ∛3.
Combine these results to get -2∛3.
Therefore, the correct response is -2∛3 or -2 3 √2.
The cube root of -16 is -2 because (-2)^3 = -16.
The cube root of 3 is ∛3.
Combine these results to get -2∛3.
Therefore, the correct response is -2∛3 or -2 3 √2.
Find the square root of 36: 36−−√ .(1 point)
Responses
6,−6
6 comma negative 6
18
18
−6
negative 6
6
Responses
6,−6
6 comma negative 6
18
18
−6
negative 6
6
The square root of 36 is 6.
So, the correct response is 6.
So, the correct response is 6.
Find the square root of 18: 18−−√ .(1 point)
Responses
9,−9
9 comma negative 9
18
18
18 is not a perfect square.
18 is not a perfect square.
9
Responses
9,−9
9 comma negative 9
18
18
18 is not a perfect square.
18 is not a perfect square.
9
The square root of 18 is not a whole number because 18 is not a perfect square.
Therefore, the correct response is "18 is not a perfect square."
Therefore, the correct response is "18 is not a perfect square."
Find the cube root of 125: 125−−−√3 .(1 point)
Responses
−5
negative 5
5
5
5,−5
5 comma negative 5
25
Responses
−5
negative 5
5
5
5,−5
5 comma negative 5
25
The cube root of 125 is 5.
Therefore, the correct response is 5.
Therefore, the correct response is 5.
Find the square root of 343.(1 point)
Responses
7–√
start root 7 end root
77–√3
7 root index 3 start root 7 end root
49
49
77
Responses
7–√
start root 7 end root
77–√3
7 root index 3 start root 7 end root
49
49
77
The square root of 343 is 7.
So, the correct response is 7.
So, the correct response is 7.
The correct answer is 7 √7
Apologies for the mistake. Let's go through the steps to find the square root of 343:
The prime factorization of 343 is 7 * 7 * 7.
Taking the square root of each factor, we have √(7 * 7 * 7).
We can simplify this as 7√7.
Therefore, the correct response is 7√7. Thank you for pointing out the error.
The prime factorization of 343 is 7 * 7 * 7.
Taking the square root of each factor, we have √(7 * 7 * 7).
We can simplify this as 7√7.
Therefore, the correct response is 7√7. Thank you for pointing out the error.
What is the circumference of a circle with a diameter of 3.75 kilometers? Estimate the circumference to the hundredths place using 3.14 as π .(1 point)
Responses
12 kilometers
12 kilometers
44.18 kilometers
44.18 kilometers
11.78 kilometers
11.78 kilometers
11.79 kilometers
Responses
12 kilometers
12 kilometers
44.18 kilometers
44.18 kilometers
11.78 kilometers
11.78 kilometers
11.79 kilometers
To find the circumference of a circle with a diameter of 3.75 kilometers, we can use the formula C = π*d, where C is the circumference and d is the diameter.
Using the given value of π as 3.14 and the diameter of 3.75 kilometers, we have:
C = 3.14 * 3.75
C ≈ 11.775.
Rounded to the hundredths place, the estimated circumference is 11.78 kilometers.
Therefore, the correct response is 11.78 kilometers.
Using the given value of π as 3.14 and the diameter of 3.75 kilometers, we have:
C = 3.14 * 3.75
C ≈ 11.775.
Rounded to the hundredths place, the estimated circumference is 11.78 kilometers.
Therefore, the correct response is 11.78 kilometers.
1 answer