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−−√
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
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.
Huh
Apologies for any confusion. Let's simplify further:
√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.
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.
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
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.
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.
Simplify 54−−√3 .
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).
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.
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)
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.
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
The square root of 169 (√169) 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.
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.
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
The cubic root of 135 (³√135) 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.
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
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.
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.
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.
Subtract 1119−−√−519−−√ .(1 point)
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.