Multiply (7–√) (−2–√) . Give an exact answer
To simplify the expression, we can use the distributive property of multiplication.
(7 – √)-2 – √) = (7 * -2) + (7 * √) + (-√ * -2) + (-√ * √)
= -14 + 7√ + 2√ + √^2
= -14 + 9√ + √^2
Since √^2 = (√)^2 = 2, we have:
= -14 + 9√ + 2
= -12 + 9√
Therefore, the exact answer is -12 + 9√.
Multiply (7–√) (−2–√) . Give an exact answer.
Responses −14−−√ negative start root
14 end root
−72–√ negative 7 start root 2 end root
5–√ start root 5 end root 14−−√
To multiply (7–√)(−2–√), we can use the distributive property.
First, multiply 7 with -2:
7 * -2 = -14.
Next, multiply 7 with -√:
7 * -√ = -7√.
Then, multiply -√ with -2:
-√ * -2 = 2√.
Finally, multiply -√ with -√:
-√ * -√ = √ * √ = √^2 = 2.
Putting it all together, we have:
(-14) + (-7√) + (2√) + 2
= -14 - 5√ + 2
= -12 - 5√.
Therefore, the exact answer is -12 - 5√.
Divide 86√2 . Provide an exact answer.(1 point)
Responses
a 43–√ 4 start root 3 end root
b 46–√ 4 start root 6 end root 83–√
c 8 start root 3 end root
d This expression is already simplified and cannot be divided further.
To divide 86√2, we need to simplify the expression further.
We can divide 86 by the square root of 2:
86 ÷ √2 = 86/√2
To rationalize the denominator, we can multiply both the numerator and denominator by the conjugate of √2, which is √2. This will eliminate the square root in the denominator.
(86/√2) * (√2/√2) = (86√2) / (2)
Dividing 86√2 by 2:
(86√2) / 2 = 43√2
Therefore, the exact answer is 43√2, which is option a) 43–√4 start root 3 end root.
To multiply (7–√) by (−2–√), you can use the FOIL method.
FOIL stands for First, Outer, Inner, Last.
First: Multiply the first terms of each binomial:
7 * -2 = -14
Outer: Multiply the outer terms of each binomial:
7 * -√ = -7√
Inner: Multiply the inner terms of each binomial:
-√ * -2 = 2√
Last: Multiply the last terms of each binomial:
-√ * -√ = √ * √ = √^2 = 1
Now, we can combine the results from the above steps:
-14 - 7√ + 2√ + 1
Simplifying:
-14 - 5√ + 1
Combining like terms:
-13 - 5√
So, the exact answer for (7–√) (−2–√) is -13 - 5√.
To multiply (7–√) and (−2–√) together, you can use the distributive property to simplify the expression. Let's break it down step by step:
(7–√)(−2–√)
First, distribute 7 to both terms in the second parentheses:
7(-2) + 7(-√)
This simplifies to:
-14 + (-7√)
Next, distribute −√ to both terms in the first parentheses:
-14√ + 7(√)
Now, let's combine like terms:
-14 + (-7√) - 14√ + 7√
Combine the terms with √:
(-7 - 14)√
Simplify the coefficient:
-21√
So, the exact answer of (7–√)(−2–√) is -21√.