To simplify the expression 5√10 + √10, we can combine the square roots that have the same radicand, which is 10 in this case.
5√10 + √10 = (5 + 1)√10 = 6√10
Therefore, the answer is d: 6√10.
add 5√10+ √10
a:√60 b:6√20 c:√25 d:6√10
23 answers
subtract 11√19 - 5√19. this difference is ?
To subtract 11√19 - 5√19, we can combine the square roots that have the same radicand, which is 19 in this case.
11√19 - 5√19 = (11 - 5)√19 = 6√19
Therefore, the difference is 6√19.
11√19 - 5√19 = (11 - 5)√19 = 6√19
Therefore, the difference is 6√19.
multiply (5√19) (6√2) give the exact answer
To multiply (5√19) (6√2), we can multiply the coefficients (5 and 6) and the square roots (√19 and √2) separately.
5√19 multiplied by 6√2 is:
(5 * 6) * (√19 * √2) = 30 * √(19 * 2) = 30√38
Therefore, the exact answer is 30√38.
5√19 multiplied by 6√2 is:
(5 * 6) * (√19 * √2) = 30 * √(19 * 2) = 30√38
Therefore, the exact answer is 30√38.
divide √95/ 3√5 whats the exact answer
To divide √95 by 3√5, we can rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator.
√95 / 3√5 = (√95 / 3√5) * (√5 / √5) = (√475 / (3√5 * √5))
Simplifying further, we get:
(√475 / (3 * √25)) = (√475 / (3 * 5)) = (√475 / 15)
Therefore, the exact answer is (√475 / 15).
√95 / 3√5 = (√95 / 3√5) * (√5 / √5) = (√475 / (3√5 * √5))
Simplifying further, we get:
(√475 / (3 * √25)) = (√475 / (3 * 5)) = (√475 / 15)
Therefore, the exact answer is (√475 / 15).
divide 36√39/ 9√13 exact answers
To divide 36√39 by 9√13, we can rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator.
(36√39) / (9√13) = [(36√39) / (9√13)] * [(√13) / (√13)]
Simplifying the numerator, we have:
36√39 * √13 = 36√(39 * 13) = 36√(507)
Now, simplifying the denominator:
9√13 * √13 = 9√(13 * 13) = 9√169 = 9 * 13 = 117
So the final result is:
(36√39) / (9√13) = (36√(507)) / 117
Therefore, the exact answer is (36√(507)) / 117.
(36√39) / (9√13) = [(36√39) / (9√13)] * [(√13) / (√13)]
Simplifying the numerator, we have:
36√39 * √13 = 36√(39 * 13) = 36√(507)
Now, simplifying the denominator:
9√13 * √13 = 9√(13 * 13) = 9√169 = 9 * 13 = 117
So the final result is:
(36√39) / (9√13) = (36√(507)) / 117
Therefore, the exact answer is (36√(507)) / 117.
simplify √48
To simplify √48, we need to find the largest perfect square that is a factor of 48. In this case, the largest perfect square that is a factor of 48 is 16.
√48 = √(16 * 3)
We can break down the square root by separating the factors:
√(16 * 3) = √16 * √3 = 4√3
Therefore, √48 simplifies to 4√3.
√48 = √(16 * 3)
We can break down the square root by separating the factors:
√(16 * 3) = √16 * √3 = 4√3
Therefore, √48 simplifies to 4√3.
simplify ^3√54
To simplify the cube root (∛) of 54, we need to find the factors of 54.
The prime factorization of 54 is 2 * 3^3.
We can then rewrite 54 as (2 * 3^3) = (2 * 27).
Taking the cube root, we can simplify this expression:
^3√54 = ^3√(2 * 3^3) = ^3√(2 * 27).
Since 27 is a perfect cube, we can simplify further:
^3√(2 * 27) = ^3√(54) = 3√2.
Therefore, the simplified form of ^3√54 is 3√2.
The prime factorization of 54 is 2 * 3^3.
We can then rewrite 54 as (2 * 3^3) = (2 * 27).
Taking the cube root, we can simplify this expression:
^3√54 = ^3√(2 * 3^3) = ^3√(2 * 27).
Since 27 is a perfect cube, we can simplify further:
^3√(2 * 27) = ^3√(54) = 3√2.
Therefore, the simplified form of ^3√54 is 3√2.
what is the irrational square root √63 rewritten as the product of integer and another irrational square root in the simplest form
To rewrite √63 as the product of an integer and another irrational square root in the simplest form, we need to find the largest perfect square that is a factor of 63. In this case, the largest perfect square that is a factor of 63 is 9.
√63 = √(9 * 7)
We can break down the square root by separating the factors:
√(9 * 7) = √9 * √7 = 3√7
Therefore, √63 can be rewritten as 3√7 in the simplest form.
√63 = √(9 * 7)
We can break down the square root by separating the factors:
√(9 * 7) = √9 * √7 = 3√7
Therefore, √63 can be rewritten as 3√7 in the simplest form.
What is the irrational cube root ^3√18 rewritten as a product of an integer and another irrational cube root ?
Find the square root of 169: √169
Find the cube root of -729: ^3√-729
Find the cube root of -8: ^3√-8
Find the cubic root of 135
What is the circumference of a circle with a diameter 4.5 miles. Estimate the circumference to the hundredths place using 3.14 for π
Rewrite the irrational cube root ^3√189 as the product of an integer and another cube root show work
Find the square root of 169: √169
Find the cube root of -729: ^3√-729
Find the cube root of -8: ^3√-8
Find the cubic root of 135
What is the circumference of a circle with a diameter 4.5 miles. Estimate the circumference to the hundredths place using 3.14 for π
Rewrite the irrational cube root ^3√189 as the product of an integer and another cube root show work
To rewrite the irrational cube root ^3√18 as a product of an integer and another irrational cube root, we need to find the largest perfect cube that is a factor of 18. In this case, the largest perfect cube that is a factor of 18 is 2.
^3√18 = ^3√(2 * 9)
We can break down the cube root by separating the factors:
^3√(2 * 9) = ^3√2 * ^3√9 = 2√9
Therefore, ^3√18 can be rewritten as 2√9.
To find the square root of 169: √169, we simply take the positive square root since the square root of any positive number is always positive.
√169 = 13
The cube root of -729: ^3√-729, can be rewritten as -9, because -9 * -9 * -9 = -729.
The cube root of -8: ^3√-8 can be rewritten as -2, because -2 * -2 * -2 = -8.
The cubic root of 135 can be expressed as ^3√135.
To find the circumference of a circle with a diameter of 4.5 miles, we can use the formula:
circumference = π * diameter
Using π ≈ 3.14 and a diameter of 4.5 miles:
circumference ≈ 3.14 * 4.5 ≈ 14.13 miles
Therefore, the estimated circumference is 14.13 miles.
To rewrite the irrational cube root ^3√189 as the product of an integer and another cube root, we need to find the largest perfect cube that is a factor of 189. In this case, the largest perfect cube that is a factor of 189 is 27.
^3√189 = ^3√(27 * 7)
We can break down the cube root by separating the factors:
^3√(27 * 7) = ^3√27 * ^3√7 = 3√27 * ^3√7 = 3 * ^3√7
Therefore, ^3√189 can be rewritten as 3 * ^3√7.
^3√18 = ^3√(2 * 9)
We can break down the cube root by separating the factors:
^3√(2 * 9) = ^3√2 * ^3√9 = 2√9
Therefore, ^3√18 can be rewritten as 2√9.
To find the square root of 169: √169, we simply take the positive square root since the square root of any positive number is always positive.
√169 = 13
The cube root of -729: ^3√-729, can be rewritten as -9, because -9 * -9 * -9 = -729.
The cube root of -8: ^3√-8 can be rewritten as -2, because -2 * -2 * -2 = -8.
The cubic root of 135 can be expressed as ^3√135.
To find the circumference of a circle with a diameter of 4.5 miles, we can use the formula:
circumference = π * diameter
Using π ≈ 3.14 and a diameter of 4.5 miles:
circumference ≈ 3.14 * 4.5 ≈ 14.13 miles
Therefore, the estimated circumference is 14.13 miles.
To rewrite the irrational cube root ^3√189 as the product of an integer and another cube root, we need to find the largest perfect cube that is a factor of 189. In this case, the largest perfect cube that is a factor of 189 is 27.
^3√189 = ^3√(27 * 7)
We can break down the cube root by separating the factors:
^3√(27 * 7) = ^3√27 * ^3√7 = 3√27 * ^3√7 = 3 * ^3√7
Therefore, ^3√189 can be rewritten as 3 * ^3√7.
What is the irrational cube root ^3√81 rewritten as a product of an integer and another irrational cube root ?
To rewrite the irrational cube root ^3√81 as a product of an integer and another irrational cube root, we need to find the largest perfect cube that is a factor of 81. In this case, the largest perfect cube that is a factor of 81 is 27.
^3√81 = ^3√(27 * 3)
We can break down the cube root by separating the factors:
^3√(27 * 3) = ^3√27 * ^3√3 = 3 * ^3√3
Therefore, ^3√81 can be rewritten as 3 * ^3√3.
^3√81 = ^3√(27 * 3)
We can break down the cube root by separating the factors:
^3√(27 * 3) = ^3√27 * ^3√3 = 3 * ^3√3
Therefore, ^3√81 can be rewritten as 3 * ^3√3.
find the cubic root of 135
a:3√5
b:3 ^3√5
c:5 ^3√27
d:^3√5
a:3√5
b:3 ^3√5
c:5 ^3√27
d:^3√5
To find the cubic root of 135, we can express it as ^3√135.
To simplify this radical, we can break down 135 into its prime factors: 135 = 3 * 3 * 3 * 5.
Therefore, ^3√135 = ^3√(3 * 3 * 3 * 5) = ^3√(3^3 * 5)
We can rewrite this as the product of an integer (3) and another cubic root:
^3√(3^3 * 5) = 3 * ^3√5.
Thus, the cubic root of 135 is 3 * ^3√5.
The correct option is d: ^3√5.
To simplify this radical, we can break down 135 into its prime factors: 135 = 3 * 3 * 3 * 5.
Therefore, ^3√135 = ^3√(3 * 3 * 3 * 5) = ^3√(3^3 * 5)
We can rewrite this as the product of an integer (3) and another cubic root:
^3√(3^3 * 5) = 3 * ^3√5.
Thus, the cubic root of 135 is 3 * ^3√5.
The correct option is d: ^3√5.
put this into easier words:
To rewrite the irrational cube root ^3√189 as the product of an integer and another cube root, we need to find the largest perfect cube that is a factor of 189. In this case, the largest perfect cube that is a factor of 189 is 27.
^3√189 = ^3√(27 * 7)
We can break down the cube root by separating the factors:
^3√(27 * 7) = ^3√27 * ^3√7 = 3√27 * ^3√7 = 3 * ^3√7
Therefore, ^3√189 can be rewritten as 3 * ^3√7.
To rewrite the irrational cube root ^3√189 as the product of an integer and another cube root, we need to find the largest perfect cube that is a factor of 189. In this case, the largest perfect cube that is a factor of 189 is 27.
^3√189 = ^3√(27 * 7)
We can break down the cube root by separating the factors:
^3√(27 * 7) = ^3√27 * ^3√7 = 3√27 * ^3√7 = 3 * ^3√7
Therefore, ^3√189 can be rewritten as 3 * ^3√7.
To rewrite the cube root of 189 (^3√189) as a product of an integer and another cube root, we look for a perfect cube that can be factored out of 189. The largest perfect cube that goes into 189 is 27.
So, we can write 189 as the product of 27 and 7: 189 = 27 * 7.
Now, we can simplify the cube root expression by separating the factors:
^3√(27 * 7) = ^3√27 * ^3√7.
Since 27 is a perfect cube, we can simplify the cube root of 27 to be just 3.
Therefore, ^3√189 can be rewritten as 3 * ^3√7.
So, we can write 189 as the product of 27 and 7: 189 = 27 * 7.
Now, we can simplify the cube root expression by separating the factors:
^3√(27 * 7) = ^3√27 * ^3√7.
Since 27 is a perfect cube, we can simplify the cube root of 27 to be just 3.
Therefore, ^3√189 can be rewritten as 3 * ^3√7.