Add 510−−√ + 10−−√ .(1 point)
Responses
60−−√
Start Root 60 End Root
25−−√
Start Root 25 End Root
610−−√
6 Start Root10 And Root
620−−√
39 answers
6 Start Root 20 And Root
Multiply (519 −−−√ ) (62–√) . Give an exact answer.(1 point)
To find the exact answer, we can simplify the square roots first.
√519 can be written as √(3 * 173) which can further be written as (√3)(√173).
Similarly, √62 can be written as √(2 * 31) which can further be written as (√2)(√31).
Now we can multiply (√3)(√173) and (√2)(√31) to get the exact answer:
(√3)(√173)(√2)(√31)
= (√3 * √2)(√173 * √31)
= √6 * √5413
Therefore, the exact answer is √6 * √5413.
√519 can be written as √(3 * 173) which can further be written as (√3)(√173).
Similarly, √62 can be written as √(2 * 31) which can further be written as (√2)(√31).
Now we can multiply (√3)(√173) and (√2)(√31) to get the exact answer:
(√3)(√173)(√2)(√31)
= (√3 * √2)(√173 * √31)
= √6 * √5413
Therefore, the exact answer is √6 * √5413.
Huh
Apologies for any confusion. Let's simplify further:
√6 * √5413
= √(6 * 5413)
= √32478
So, the exact answer is √32478.
√6 * √5413
= √(6 * 5413)
= √32478
So, the exact answer is √32478.
Divide 95√35√ . Provide an exact answer. (1 point)
To divide, we can simplify the square roots first.
Starting with √35, we can break it down as follows:
√35 = √(5 * 7)
Therefore, we have:
95√35 = 95√(5 * 7)
Since we are dividing by √35, this is the same as multiplying by its reciprocal:
(95√(5 * 7)) / √35 = (95√(5 * 7)) * (1 / √35)
Now, let's simplify further:
= (95 * √5 * √7) * (1 / (√5 * √7))
We can simplify further by canceling out the square roots of 5 and 7:
= (95 * √5 * √7) * (1 / (√5 * √7))
= 95
Therefore, the exact answer is 95.
Starting with √35, we can break it down as follows:
√35 = √(5 * 7)
Therefore, we have:
95√35 = 95√(5 * 7)
Since we are dividing by √35, this is the same as multiplying by its reciprocal:
(95√(5 * 7)) / √35 = (95√(5 * 7)) * (1 / √35)
Now, let's simplify further:
= (95 * √5 * √7) * (1 / (√5 * √7))
We can simplify further by canceling out the square roots of 5 and 7:
= (95 * √5 * √7) * (1 / (√5 * √7))
= 95
Therefore, the exact answer is 95.
Divide 3639√913√ . Provide an exact answer. (1 point)
To divide, we need to simplify the square roots first.
Starting with √913, we can break it down as follows:
√913 = √(11 * 83)
Therefore, we have:
3639√913 = 3639√(11 * 83)
Since we are dividing by √913, this is the same as multiplying by its reciprocal:
(3639√(11 * 83)) / √913 = (3639√(11 * 83)) * (1 / √(11 * 83))
Now, let's simplify further:
= (3639 * √11 * √83) * (1 / (√11 * √83))
We can simplify further by canceling out the square roots of 11 and 83:
= (3639 * √11 * √83) * (1 / (√11 * √83))
= 3639
Therefore, the exact answer is 3639.
Starting with √913, we can break it down as follows:
√913 = √(11 * 83)
Therefore, we have:
3639√913 = 3639√(11 * 83)
Since we are dividing by √913, this is the same as multiplying by its reciprocal:
(3639√(11 * 83)) / √913 = (3639√(11 * 83)) * (1 / √(11 * 83))
Now, let's simplify further:
= (3639 * √11 * √83) * (1 / (√11 * √83))
We can simplify further by canceling out the square roots of 11 and 83:
= (3639 * √11 * √83) * (1 / (√11 * √83))
= 3639
Therefore, the exact answer is 3639.
Huh
Apologies for any confusion. Let's simplify further:
√11 * √83 cannot be simplified any further because 11 and 83 are both prime numbers.
Therefore, the exact answer is:
3639√11√83
√11 * √83 cannot be simplified any further because 11 and 83 are both prime numbers.
Therefore, the exact answer is:
3639√11√83
Simplify 48−−√ .(1 point)
To simplify √48, we can break it down into prime factors:
48 = 2 * 2 * 2 * 2 * 3 = 2^4 * 3
Using the property of square roots (√a * b = √a * √b), we can simplify √48:
√48 = √(2^4 * 3) = 2^2 * √3 = 4√3
Therefore, the simplified form of √48 is 4√3.
48 = 2 * 2 * 2 * 2 * 3 = 2^4 * 3
Using the property of square roots (√a * b = √a * √b), we can simplify √48:
√48 = √(2^4 * 3) = 2^2 * √3 = 4√3
Therefore, the simplified form of √48 is 4√3.
What
Apologies for the errors in my previous response. Let's correct it:
To simplify √48, we can factorize 48 as follows:
48 = 2 * 2 * 2 * 2 * 3 = 2^4 * 3
Now, we can simplify the square root:
√48 = √(2^4 * 3) = √(2^4) * √3 = 2^2 * √3 = 4√3
Therefore, the simplified form of √48 is 4√3.
To simplify √48, we can factorize 48 as follows:
48 = 2 * 2 * 2 * 2 * 3 = 2^4 * 3
Now, we can simplify the square root:
√48 = √(2^4 * 3) = √(2^4) * √3 = 2^2 * √3 = 4√3
Therefore, the simplified form of √48 is 4√3.
Simplify 54−−√3 .
Note: You will find the option to add a cubic root symbol in the Algebra ( ×
) keyboard.
Note: You will find the option to add a cubic root symbol in the Algebra ( ×
) keyboard.
To simplify √(54√3), we can break it down into a product of two separate square roots:
√(54√3) = √54 * √√3
Now, let's simplify each square root individually:
First, let's simplify √54. We can factorize 54 as follows:
54 = 2 * 3^3 = 2 * 3 * 3 * 3
Taking the square root of each factor:
√54 = √(2 * 3 * 3 * 3) = √(2 * 3^3) = √2 * 3√3
Next, let's simplify √√3. Taking the square root of a square root cancels out the square root:
√√3 = (√3)^(1/2) = 3^(1/4)
Combining the simplified forms:
√(54√3) = (√2 * 3√3) * 3^(1/4)
Therefore, the simplified form of √(54√3) is (√2 * 3√3) * 3^(1/4).
√(54√3) = √54 * √√3
Now, let's simplify each square root individually:
First, let's simplify √54. We can factorize 54 as follows:
54 = 2 * 3^3 = 2 * 3 * 3 * 3
Taking the square root of each factor:
√54 = √(2 * 3 * 3 * 3) = √(2 * 3^3) = √2 * 3√3
Next, let's simplify √√3. Taking the square root of a square root cancels out the square root:
√√3 = (√3)^(1/2) = 3^(1/4)
Combining the simplified forms:
√(54√3) = (√2 * 3√3) * 3^(1/4)
Therefore, the simplified form of √(54√3) is (√2 * 3√3) * 3^(1/4).
What is the irrational square root 63−−√ rewritten as the product of an integer and another irrational square root, in simplest form?(1 point)
To simplify √63, we can factorize 63 into prime factors:
63 = 3 * 3 * 7
Now we can simplify the square root:
√63 = √(3 * 3 * 7)
Taking out pairs of the same factor from the square root:
√(3 * 3 * 7) = √(3 * 3) * √7
Simplifying the square roots:
√(3 * 3) = 3
√7 remains the same
So, the simplified form of √63 is 3√7.
Therefore, the irrational square root √63 can be rewritten as the product of an integer and another irrational square root, in simplest form, as 3√7.
63 = 3 * 3 * 7
Now we can simplify the square root:
√63 = √(3 * 3 * 7)
Taking out pairs of the same factor from the square root:
√(3 * 3 * 7) = √(3 * 3) * √7
Simplifying the square roots:
√(3 * 3) = 3
√7 remains the same
So, the simplified form of √63 is 3√7.
Therefore, the irrational square root √63 can be rewritten as the product of an integer and another irrational square root, in simplest form, as 3√7.
What is the irrational cube root 81−−√3 rewritten as a product of an integer and another irrational cube root?
Note: You will find the option to add a cubic root symbol in the Algebra ( ×
) keyboard.
(1 point)
Note: You will find the option to add a cubic root symbol in the Algebra ( ×
) keyboard.
(1 point)
To simplify the cube root of 81 (∛81), we need to find the prime factorization of 81:
81 = 3 * 3 * 3 * 3 = 3^4
Now, let's rewrite the cube root:
∛81 = ∛(3^4)
We can rewrite this as a product of an integer and another irrational cube root by separating out one cube root of 3:
∛(3^4) = ∛(3^3 * 3) = ∛(27 * 3)
Now, simplifying the cube roots:
∛(27 * 3) = (∛27) * (∛3) = 3 * (∛3)
Therefore, the irrational cube root of 81 (∛81) can be rewritten as a product of an integer and another irrational cube root as 3∛3.
81 = 3 * 3 * 3 * 3 = 3^4
Now, let's rewrite the cube root:
∛81 = ∛(3^4)
We can rewrite this as a product of an integer and another irrational cube root by separating out one cube root of 3:
∛(3^4) = ∛(3^3 * 3) = ∛(27 * 3)
Now, simplifying the cube roots:
∛(27 * 3) = (∛27) * (∛3) = 3 * (∛3)
Therefore, the irrational cube root of 81 (∛81) can be rewritten as a product of an integer and another irrational cube root as 3∛3.
Find the square root of 169: 169−−−√ .(1 point)
Responses
−13
negative 13
84.5
84.5
13,−13
13 comma negative 13
13
13
Responses
−13
negative 13
84.5
84.5
13,−13
13 comma negative 13
13
13
The square root of 169 (√169) is 13.
Therefore, the correct response is 13.
Therefore, the correct response is 13.
Find the cube root of −729 : −729−−−−√3 (1 point
The cube root of -729 (−729√3) is -9.
Therefore, the correct response is -9.
Therefore, the correct response is -9.
Find the cube root of −8 : −8−−−√3 (1 point)
The cube root of -8 (−8√3) is -2.
Therefore, the correct response is -2.
Therefore, the correct response is -2.
Find the cubic root of 135.(1 point)
Responses
5–√3
root index 3 start root 5 end root
35–√
3 start root 5 end root
35–√3
3 root index 3 start root 5 end root
527−−√3
Responses
5–√3
root index 3 start root 5 end root
35–√
3 start root 5 end root
35–√3
3 root index 3 start root 5 end root
527−−√3
The cubic root of 135 (³√135) is 5√3.
Therefore, the correct response is 5√3.
Therefore, the correct response is 5√3.
So
I apologize for the incorrect response. Let's simplify the cubic root of 135 correctly.
To find the cubic root of 135 (³√135), we can write 135 as a product of prime factors:
135 = 3 * 3 * 3 * 5
Now we can simplify the cubic root:
³√135 = ³√(3 * 3 * 3 * 5)
Taking out groups of three equal factors from the cubic root:
³√(3 * 3 * 3 * 5) = ³√(3 * 3 * 3) * ³√5
Simplifying the cubic roots:
³√(3 * 3 * 3) = ³√27 = 3
³√5 remains the same
So, the simplified form of the cubic root of 135 is 3√5.
Therefore, the correct response is 3√5.
To find the cubic root of 135 (³√135), we can write 135 as a product of prime factors:
135 = 3 * 3 * 3 * 5
Now we can simplify the cubic root:
³√135 = ³√(3 * 3 * 3 * 5)
Taking out groups of three equal factors from the cubic root:
³√(3 * 3 * 3 * 5) = ³√(3 * 3 * 3) * ³√5
Simplifying the cubic roots:
³√(3 * 3 * 3) = ³√27 = 3
³√5 remains the same
So, the simplified form of the cubic root of 135 is 3√5.
Therefore, the correct response is 3√5.
What is the circumference of a circle with a diameter of 4.5 miles? Estimate the circumference to the hundredths place using 3.14 for π
.(1 point)
Responses
14.2 miles
14.2 miles
14.13 miles
14.13 miles
7.07 miles
7.07 miles
63.59 miles
.(1 point)
Responses
14.2 miles
14.2 miles
14.13 miles
14.13 miles
7.07 miles
7.07 miles
63.59 miles
The circumference of a circle can be found using the formula C = πd, where C is the circumference and d is the diameter.
Given a diameter of 4.5 miles, we can calculate the circumference using the value 3.14 for π:
C = 3.14 * 4.5
C ≈ 14.13
Therefore, the circumference of a circle with a diameter of 4.5 miles, estimated to the hundredths place using 3.14 for π, is approximately 14.13 miles.
The correct response is 14.13 miles.
Given a diameter of 4.5 miles, we can calculate the circumference using the value 3.14 for π:
C = 3.14 * 4.5
C ≈ 14.13
Therefore, the circumference of a circle with a diameter of 4.5 miles, estimated to the hundredths place using 3.14 for π, is approximately 14.13 miles.
The correct response is 14.13 miles.
Rewrite the irrational cube root 189−−−√3 as the product of an integer and another irrational cube root. Show your work.
Note: You will find the option to add a cubic root symbol in the Algebra ( ×
) keyboard.
Note: You will find the option to add a cubic root symbol in the Algebra ( ×
) keyboard.
To rewrite the cube root of 189 (∛189) as the product of an integer and another irrational cube root, we'll first need to find the prime factorization of 189.
189 = 3 * 3 * 3 * 7
Now, let's rewrite the cube root:
∛189 = ∛(3 * 3 * 3 * 7)
We can extract one cube root of 3 from 189:
∛(3 * 3 * 3 * 7) = ∛(3 * 3 * 3) * ∛7
Simplifying the cube roots:
∛(3 * 3 * 3) = ∛(27) = 3
∛7 remains the same
So, the irrational cube root of 189 (∛189) can be rewritten as the product of an integer and another irrational cube root as 3∛7.
Therefore, the irrational cube root ∛189 is rewritten as the product 3∛7.
189 = 3 * 3 * 3 * 7
Now, let's rewrite the cube root:
∛189 = ∛(3 * 3 * 3 * 7)
We can extract one cube root of 3 from 189:
∛(3 * 3 * 3 * 7) = ∛(3 * 3 * 3) * ∛7
Simplifying the cube roots:
∛(3 * 3 * 3) = ∛(27) = 3
∛7 remains the same
So, the irrational cube root of 189 (∛189) can be rewritten as the product of an integer and another irrational cube root as 3∛7.
Therefore, the irrational cube root ∛189 is rewritten as the product 3∛7.
Subtract 1119−−√−519−−√ .(1 point)
The difference is .
The difference is .
To subtract √1119 from √519, we have to simplify each square root individually:
√1119 is not a perfect square, so we can't simplify it further.
√519 can be simplified by breaking it down into prime factors:
519 = 3 * 173
Therefore, √519 = √(3 * 173) = √3 * √173.
Now, let's subtract the two square roots:
√519 - √1119 = (√3 * √173) - √1119.
Since the two square roots don't have any common factors, we cannot simplify the expression any further.
Therefore, the difference between √1119 and √519 is (√3 * √173) - √1119.
√1119 is not a perfect square, so we can't simplify it further.
√519 can be simplified by breaking it down into prime factors:
519 = 3 * 173
Therefore, √519 = √(3 * 173) = √3 * √173.
Now, let's subtract the two square roots:
√519 - √1119 = (√3 * √173) - √1119.
Since the two square roots don't have any common factors, we cannot simplify the expression any further.
Therefore, the difference between √1119 and √519 is (√3 * √173) - √1119.
All of the answers:
1. 6√10
2. 6√19
3. 30√38
4. √19/3
5. 4√3
6. 4√3
7. 3 ^3√2
8. 3√7
9. 3 ^3√3
10. 13
11. -9
12. -2
13. 3 ^3√5
14. 14.13 miles
15. GOOD LUCK i tried so I'll let you know if its correct and if this isn't correct i hope you find out i will get a grading for this rq and I'll come back and at least give an idea of what you will write. :3
1. 6√10
2. 6√19
3. 30√38
4. √19/3
5. 4√3
6. 4√3
7. 3 ^3√2
8. 3√7
9. 3 ^3√3
10. 13
11. -9
12. -2
13. 3 ^3√5
14. 14.13 miles
15. GOOD LUCK i tried so I'll let you know if its correct and if this isn't correct i hope you find out i will get a grading for this rq and I'll come back and at least give an idea of what you will write. :3
so is this correct???