multiply (√7) (-√2). give an exact answer
To multiply (√7) (-√2), we can simplify by multiplying the coefficients and keeping the square roots separate.
(√7) (-√2) = -√14
Therefore, the exact answer is -√14.
To multiply (√7) and (-√2) and obtain an exact answer, follow these steps:
Step 1: Simplify each square root individually:
√7 cannot be simplified further because 7 does not have any perfect square factors.
√2 can be simplified as follows:
√2 = √(2 * 1) = √2 * √1 = √2
So, the expression becomes:
(√7) * (-√2) = √7 * √2
Step 2: Multiply the coefficients and simplify the product:
√7 * √2 = √(7 * 2) = √14
Therefore, the exact answer is √14.
To multiply (√7) and (-√2) and obtain an exact answer, follow these steps:
Step 1: Simplify the individual square roots.
- (√7) is the square root of 7.
- (-√2) is the negative square root of 2.
Step 2: Multiply the values outside of the square roots.
- Since we have (-√2), the value outside the square root is -1.
- Multiply -1 with √7 to get -√7.
Step 3: Multiply the values inside the square roots, which results in √14.
Step 4: Combine the results from Steps 2 and 3.
- (-√7) times (√14) = -√(7*14).
So, the exact answer for the expression (√7) (-√2) is -√(7*14), which can be further simplified as -√98.
divide 8√6/2. provide an exact answer
To divide 8√6 by 2, we can simplify the expression as follows:
8√6 / 2 = (8/2) * √6 = 4√6
Therefore, the exact answer is 4√6.
divide 4√10/√2 provide an exact answer
To divide 4√10 by √2, we can simplify the expression as follows:
4√10 / √2 = (4/1) * (√10/√2) = 4 * (√10/√2)
Next, we rationalize the denominator by multiplying both the numerator and denominator by √2:
4 * (√10/√2) * (√2/√2) = (4 * √10 * √2) / (1 * 2) = (4√20) / 2 = 2√20
Therefore, the exact answer is 2√20.
thats not right
Apologies for the earlier incorrect response. Let's correct the calculation:
To divide 4√10 by √2, we can simplify the expression as follows:
(4√10)/√2 = (4/1) * (√10/√2) = 4 * (√10/√2)
Next, we rationalize the denominator by multiplying both the numerator and denominator by √2:
4 * (√10/√2) * (√2/√2) = (4 * √10 * √2) / (√2 * √2) = (4√20) / 2 = 2√20 / 2 = √20
Therefore, the correct exact answer is √20.
the options are 2√10, 4√5, 2√5, or it cant be divided further
Apologies for the confusion. Let's re-evaluate the division:
We have:
(4√10) / √2
To divide, we can simplify by rationalizing the denominator. Multiply both the numerator and denominator by √2:
((4√10) / √2) * (√2 / √2) = (4√(10*2)) / √(2*2) = (4√20) / √4 = 4√20 / 2 = 2√20
Therefore, the correct exact answer is 2√20.
However, we can simplify √20 further. √20 = √(4 * 5) = √4 * √5 = 2√5.
So, the accurate exact answer is 2√5.
Apologies for the earlier incorrect response.
simplify √300
To simplify √300, we can factor 300 into its prime factors:
300 = 2 * 2 * 3 * 5 * 5
Next, simplify the square root by taking out pairs of the same prime factors:
√300 = √(2 * 2 * 3 * 5 * 5)
= √[(2 * 2) * (3) * (5 * 5)]
= 2 * 5 * √(3)
= 10√3
Therefore, √300 simplifies to 10√3.
simplify 13√27
To simplify 13√27, we can factor 27 into its prime factors:
27 = 3 * 3 * 3
Next, simplify the square root by taking out pairs of the same prime factors:
13√27 = 13√(3 * 3 * 3)
= 13 * √(3 * 3) * √3
= 13 * 3 * √3
= 39√3
Therefore, 13√27 simplifies to 39√3.