11√19 - 5√19
whats the difference?
29 answers
The difference between 11√19 and 5√19 is 6√19.
multiply (5√19) (6√2) give an exact answer
To multiply (5√19) and (6√2), we can apply the distributive property.
(5√19) (6√2) = 5*6*(√19*√2) = 30√(19*2) = 30√38
Therefore, the exact answer is 30√38.
(5√19) (6√2) = 5*6*(√19*√2) = 30√(19*2) = 30√38
Therefore, the exact answer is 30√38.
simplify √48
To simplify √48, we need to find the largest perfect square that is a factor of 48. We can see that 16 is the largest perfect square that divides 48.
√48 = √(16 * 3)
Since the square root can be distributed over multiplication, we can simplify further:
√(16 * 3) = √16 * √3 = 4√3
Therefore, √48 simplifies to 4√3.
√48 = √(16 * 3)
Since the square root can be distributed over multiplication, we can simplify further:
√(16 * 3) = √16 * √3 = 4√3
Therefore, √48 simplifies to 4√3.
simplify 3^√54
To simplify 3^√54, we can rewrite 54 as a product of perfect square factors:
54 = 9 * 6 = 3^2 * 2 * 3
Now we can rewrite 3^√54 using exponent rules:
3^√54 = 3^(√(3^2 * 2 * 3))
Since the square root (denoted by √) and the exponent of 2 are inverse operations, we can simplify further:
3^(√(3^2 * 2 * 3)) = 3^(√(3^2) * √(2) * √(3))
Since √(3^2) is simply 3 and √(2) and √(3) cannot be simplified further, we have:
3^(√(3^2) * √(2) * √(3)) = 3^(3 * √(2) * √(3))
Therefore, the simplified form of 3^√54 is 3^(3 * √(2) * √(3)).
54 = 9 * 6 = 3^2 * 2 * 3
Now we can rewrite 3^√54 using exponent rules:
3^√54 = 3^(√(3^2 * 2 * 3))
Since the square root (denoted by √) and the exponent of 2 are inverse operations, we can simplify further:
3^(√(3^2 * 2 * 3)) = 3^(√(3^2) * √(2) * √(3))
Since √(3^2) is simply 3 and √(2) and √(3) cannot be simplified further, we have:
3^(√(3^2) * √(2) * √(3)) = 3^(3 * √(2) * √(3))
Therefore, the simplified form of 3^√54 is 3^(3 * √(2) * √(3)).
find the square root of 169: √169
The square root of 169 is 13.
what is the irrational square root √63 rewritten as the product of integer and another irrational square root, in simplest form
To rewrite √63 as the product of an integer and another irrational square root in simplest form, we need to find the largest perfect square that divides 63.
By observing, we can see that 9 is the largest perfect square that divides 63.
So, we can rewrite √63 as √(9 * 7).
Now, using the property of the square root, we can split it into two separate square roots:
√(9 * 7) = √9 * √7 = 3√7.
Therefore, √63 can be rewritten as the product of 3 and √7, in simplest form.
By observing, we can see that 9 is the largest perfect square that divides 63.
So, we can rewrite √63 as √(9 * 7).
Now, using the property of the square root, we can split it into two separate square roots:
√(9 * 7) = √9 * √7 = 3√7.
Therefore, √63 can be rewritten as the product of 3 and √7, in simplest form.
find the cubic root of 135
The cubic root of 135 is approximately 5.260.
give exact answer
To find the exact cubic root of 135, we need to determine the prime factorization of 135.
135 = 3 * 3 * 3 * 5
Now, we can group the factors in sets of three to find the cube root.
∛135 = ∛(3 * 3 * 3 * 5) = (∛3 * ∛3 * ∛3) * ∛5 = 3∛5.
Therefore, the exact cubic root of 135 is 3∛5.
135 = 3 * 3 * 3 * 5
Now, we can group the factors in sets of three to find the cube root.
∛135 = ∛(3 * 3 * 3 * 5) = (∛3 * ∛3 * ∛3) * ∛5 = 3∛5.
Therefore, the exact cubic root of 135 is 3∛5.
divide √95/3√5 provide exact answer
To divide √95 by 3√5, we can simplify by multiplying both the numerator and denominator by the conjugate of the denominator, which is √5.
√95/3√5 = (√95/3√5) * (√5/√5)
Simplifying the numerator and denominator:
= (√(95*5))/(3 * √(5*5))
= √475/3√25
= √475/3√(5*5)
= √475/3 * 5
= √475/15
Therefore, the exact answer is √475/15.
√95/3√5 = (√95/3√5) * (√5/√5)
Simplifying the numerator and denominator:
= (√(95*5))/(3 * √(5*5))
= √475/3√25
= √475/3√(5*5)
= √475/3 * 5
= √475/15
Therefore, the exact answer is √475/15.
divide 38√39/9√13
To divide 38√39 by 9√13, we can simplify by multiplying both the numerator and denominator by the conjugate of the denominator, which is √13.
(38√39)/(9√13) = (38√39)/(9√13) * (√13/√13)
Simplifying the numerator and denominator:
= (38√(39*13))/(9 * √(13*13))
= (38√(507))/(9 * 13)
= (38√(507))/(9 * 13)
= (2 * 19 * √507) / (3 * 13)
= (38 * √507)/39
Therefore, the simplified form of 38√39/9√13 is (38 * √507)/39.
(38√39)/(9√13) = (38√39)/(9√13) * (√13/√13)
Simplifying the numerator and denominator:
= (38√(39*13))/(9 * √(13*13))
= (38√(507))/(9 * 13)
= (38√(507))/(9 * 13)
= (2 * 19 * √507) / (3 * 13)
= (38 * √507)/39
Therefore, the simplified form of 38√39/9√13 is (38 * √507)/39.
find the rubic cube of -729: 3^√-729 give exact answer
To find the exact cubic root of -729, let's first determine the prime factorization of -729.
-729 can be written as -1 * 3 * 3 * 3 * 3 * 3 * 3 * 3.
Since we're looking for the cubic root, we can group the factors in sets of three:
∛(-729) = ∛(-1 * 3 * 3 * 3 * 3 * 3 * 3 * 3) = -1 * ∛(3 * 3 * 3 * 3 * 3 * 3 * 3)
We know that the cubic root of a negative number is the negative of the cubic root of the positive number. And since we have an odd number of 3's being cubed, the cube root of 3^7 will be negative:
-1 * ∛(3 * 3 * 3 * 3 * 3 * 3 * 3) = -1 * 3 * 3 = -9.
Therefore, the exact cubic root of -729 is -9.
-729 can be written as -1 * 3 * 3 * 3 * 3 * 3 * 3 * 3.
Since we're looking for the cubic root, we can group the factors in sets of three:
∛(-729) = ∛(-1 * 3 * 3 * 3 * 3 * 3 * 3 * 3) = -1 * ∛(3 * 3 * 3 * 3 * 3 * 3 * 3)
We know that the cubic root of a negative number is the negative of the cubic root of the positive number. And since we have an odd number of 3's being cubed, the cube root of 3^7 will be negative:
-1 * ∛(3 * 3 * 3 * 3 * 3 * 3 * 3) = -1 * 3 * 3 = -9.
Therefore, the exact cubic root of -729 is -9.
find the cube root of -8: 3^√-8 give exact answer
To find the exact cubic root of -8, let's first determine the prime factorization of -8.
-8 can be written as -1 * 2 * 2 * 2.
Since we're looking for the cubic root, we can group the factors in sets of three:
∛(-8) = ∛(-1 * 2 * 2 * 2) = -1 * ∛(2 * 2 * 2)
We know that the cubic root of a negative number is the negative of the cubic root of the positive number. Since we have an even number of 2's being cubed, the cube root of 2^3 will be positive:
-1 * ∛(2 * 2 * 2) = -1 * 2 = -2.
Therefore, the exact cubic root of -8 is -2.
-8 can be written as -1 * 2 * 2 * 2.
Since we're looking for the cubic root, we can group the factors in sets of three:
∛(-8) = ∛(-1 * 2 * 2 * 2) = -1 * ∛(2 * 2 * 2)
We know that the cubic root of a negative number is the negative of the cubic root of the positive number. Since we have an even number of 2's being cubed, the cube root of 2^3 will be positive:
-1 * ∛(2 * 2 * 2) = -1 * 2 = -2.
Therefore, the exact cubic root of -8 is -2.
what is the irrational square root 3^√81 rewritten as the product of integer and another irrational square root, give exact answer
To rewrite √(3^√81) as the product of an integer and another irrational square root in exact form, we need to determine the prime factorization of 81.
81 = 3 * 3 * 3 * 3 = 3^4
Now, we can rewrite √(3^√81) using the property of square roots and exponents:
√(3^√81) = √(3^4)^√1 = √(3^4) = 3^2.
Therefore, √(3^√81) can be rewritten as the product of 3 and √1, which simplifies to 3.
81 = 3 * 3 * 3 * 3 = 3^4
Now, we can rewrite √(3^√81) using the property of square roots and exponents:
√(3^√81) = √(3^4)^√1 = √(3^4) = 3^2.
Therefore, √(3^√81) can be rewritten as the product of 3 and √1, which simplifies to 3.
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 .
The circumference of a circle can be calculated using the formula C = πd, where C is the circumference and d is the diameter.
Given that the diameter is 4.5 miles, we can substitute this value into the formula:
C = 3.14 * 4.5
Calculating this, we have:
C ≈ 14.13
Therefore, the circumference of the circle is approximately 14.13 miles.
Given that the diameter is 4.5 miles, we can substitute this value into the formula:
C = 3.14 * 4.5
Calculating this, we have:
C ≈ 14.13
Therefore, the circumference of the circle is approximately 14.13 miles.
Rewrite the irrational cube root ∛189 as the product of an integer and another irrational cube root. Show your work.
To rewrite ∛189 as the product of an integer and another irrational cube root, we need to determine the prime factorization of 189.
189 can be factored as 3 * 3 * 3 * 7.
Now, let's group the factors in sets of three to find the cube root:
∛189 = ∛(3 * 3 * 3 * 7) = ∛(3^3 * 7).
Using the property of the cube root, we can simplify this further:
∛(3^3 * 7) = ∛(3^3) * ∛7 = 3∛7.
Therefore, ∛189 can be rewritten as the product of 3 and ∛7.
189 can be factored as 3 * 3 * 3 * 7.
Now, let's group the factors in sets of three to find the cube root:
∛189 = ∛(3 * 3 * 3 * 7) = ∛(3^3 * 7).
Using the property of the cube root, we can simplify this further:
∛(3^3 * 7) = ∛(3^3) * ∛7 = 3∛7.
Therefore, ∛189 can be rewritten as the product of 3 and ∛7.
1 answer