SOLUTION: Multiply. Simplify Completely (sqrt(-2) - sqrt(-27)) * (sqrt(-2) + sqrt (-75))

Algebra ->  Square-cubic-other-roots -> SOLUTION: Multiply. Simplify Completely (sqrt(-2) - sqrt(-27)) * (sqrt(-2) + sqrt (-75))      Log On


   

Question 1193093: Multiply. Simplify Completely
(sqrt(-2) - sqrt(-27)) * (sqrt(-2) + sqrt (-75))
Found 4 solutions by MathLover1, Theo, ikleyn, greenestamps:
Answer by MathLover1(20849) About Me  (Show Source):
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
(sqrt(-2) - sqrt(-27)) * (sqrt(-2) + sqrt (-75)) is equal to:
sqrt(-2) * (sqrt(-2) + sqrt (-75)) - sqrt(-27) * (sqrt(-2) + sqrt(-75)) which is equal to:
sqrt(-2) * sqrt(-2) + sqrt(-2) * sqrt(-75) - sqrt(-27) * sqrt(-2) - sqrt(-27) * sqrt(-75).

note that:

sqrt(-2) = sqrt(2) * i
sqrt(-75) = sqrt(75) * i
sqrt(-27) = sqrt(27) * i

consequently:

sqrt(-2) * sqrt(-2) + sqrt(-2) * sqrt(-75) - sqrt(-27) * sqrt(-2) - sqrt(-27) * sqrt(-75) becomes:
sqrt(2)*i * sqrt(2)*i + sqrt(2)*i * sqrt(75)*i - sqrt(27)*i * sqrt(2)*i - sqrt(27)*i * sqrt75)*i which becomes:
sqrt(2)*sqrt(2)*i^2 + sqrt(2)*sqrt(75)*i^2 - sqrt(27)*sqrt(2)*i^2 - sqrt(27)*sqrt(75)*i^2 which becomes:
sqrt(4)*i^2 + sqrt(150)*i^2 - sqrt(54)*i^2 - sqrt(2025)*i^2.

since i^2 = -1, then:

sqrt(4)*i^2 + sqrt(150)*i^2 - sqrt(54)*i^2 - sqrt(2025)*i^2 becomes:
sqrt(4)*-1 + sqrt(150)*-1 - sqrt(54)*-1 - sqrt(2025)*-1 which becomes:
-sqrt(4) - sqrt(150) + sqrt(54) + sqrt(2025) which is equal to 38.10102051.

your solution should be 38.10102051.

note that the rules of the value of i in complex arithmetic equations is:

i^1 = i
i^2 = -1
i^3 = -i
i^4 = 1

this is a repetitive pattern that repeats for every set of 4.

to determine how to analyze this for i ^ something greater than 4, an example should show you how it's done.

i^38 is the example.
divide 38 by 4 to get 9.5
9 * 4 = 36
38 minus 36 = 2
i^2 = -1
therefore i^38 = -1

Answer by ikleyn(52754) About Me  (Show Source):
You can put this solution on YOUR website!
.

The solution by MathLover1 contains arithmetic errors,

so you better ignore it, for your safety.



Answer by greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!


%28sqrt%28-2%29+-+sqrt%28-27%29%29+%2A+%28sqrt%28-2%29+%2B+sqrt+%28-75%29%29

Convert to "i" form for multiplying imaginary numbers.

%28i%2Asqrt%282%29-i%2Asqrt%2827%29%29%2A%28i%2Asqrt%282%29%2Bi%2Asqrt%2875%29%29

Simplify each term where possible.

%28i%2Asqrt%282%29-3i%2Asqrt%283%29%29%2A%28i%2Asqrt%282%29%2B5i%2Asqrt%283%29%29

%28i%28sqrt%282%29-3sqrt%283%29%29%29%28i%28sqrt%282%29%2B5sqrt%283%29%29%29



%28-1%29%282%2B5sqrt%286%29-3sqrt%286%29-45%29

%28-1%29%28-43%2B2sqrt%286%29%29

43-2sqrt%286%29

ANSWER: 43-2sqrt%286%29