Multiply 93 −−√ ⋅67–√
To multiply the given expression, we can simplify each square root individually and then multiply the simplified expressions together.
First, let's simplify √93. We can factorize 93 as 3*31, and there are no perfect squares in the factorization, so we cannot simplify it further. Therefore, √93 remains as is.
Next, let's simplify √67. There are no perfect squares in the factorization of 67, so we also cannot simplify it further.
Now, let's multiply the simplified expressions:
√93 * √67 = √(93 * 67)
Multiplying 93 and 67, we get:
√(93 * 67) = √(6249)
Now, let's simplify √6249. We can factorize 6249 as 3^2 * 11 * 59, and the square root of 3^2 is 3. Therefore, we can simplify √6249 as 3√11 * √59.
Putting it all together:
√93 * √67 = 3√11 * √59
So, the multiplication of 93 −−√ and 67–√ is given by 3√11 * √59.
Multiply 11 −−−√ ⋅67–√ . Give an exact answer.
To multiply 11 −−−√ and 67–√, we can simplify each square root individually and then multiply the simplified expressions together.
First, let's simplify −−−√11. The cube root of 11 can't be simplified further, so it remains as is.
Next, let's simplify 67–√. There are no perfect squares in the factorization of 67, so we cannot simplify it further.
Now, let's multiply the simplified expressions:
−−−√11 * 67–√ = −−−√(11 * 67)
Multiplying 11 and 67, we get:
−−−√(11 * 67) = −−−√737
The cube root of 737 cannot be simplified further, so the exact answer to the multiplication is −−−√737.
Multiply (7–√) (−2–√) . Give an exact answer.
To multiply the expressions (7–√) and (−2–√), we can use the FOIL method.
FOIL stands for: First, Outer, Inner, Last.
First, we multiply the first terms of each expression:
7 * -2 = -14.
Outer, we multiply the outer terms of each expression:
7 * -√ = -7√.
Inner, we multiply the inner terms of each expression:
-√ * -2 = 2√.
Last, we multiply the last terms of each expression:
-√ * -√ = √ * √ = (√)^2 = 1.
Now, let's combine the simplified terms:
-14 - 7√ + 2√ + 1.
Combining like terms, we have:
-14 - 5√ + 1.
Finally, simplifying further, we get:
-13 - 5√.
Therefore, the exact answer to the multiplication (7–√) (−2–√) is -13 - 5√.
Divide 8√6/2 . Provide an exact answer.
To divide 8√6 by 2, we divide the numerical coefficient 8 by 2, and divide the radical term √6 by 2 as well.
Starting with the numerical coefficient:
8 / 2 = 4.
Now, let's divide the radical:
√6 / 2 = (√6) / 2.
Since we cannot simplify the square root of 6 any further, the division remains as (√6) / 2.
Putting it all together:
8√6 / 2 = 4(√6) / 2.
Next, we can simplify the expression:
4(√6) / 2 = 2√6.
Therefore, the exact answer to 8√6 / 2 is 2√6.
divide 4√10/√2
To divide 4√10 by √2, we can simplify the expression by rationalizing the denominator.
First, let's rationalize the denominator, which means we need to eliminate the radical (√) in the denominator.
To do this, we multiply both the numerator and denominator by the conjugate of the denominator (√2). The conjugate of √2 is also √2.
So, the expression becomes:
(4√10 * √2) / (√2 * √2)
Simplifying the numerator and denominator:
(4√(10 * 2)) / (√(2 * 2))
We have:
(4 √20) / (√4)
Simplifying further:
(4 √20) / 2
Now, we can simplify the expression:
2 √20
To simplify √20, we can factorize it. 20 can be factored as 2 * 2 * 5. We can take out the √4 as a whole number, which is 2, while leaving the √5 under the square root.
Therefore, the final answer is:
2 * 2 * √5
4√5
Thus, 4√10 / √2 simplifies to 4√5.