[2sqrt(2) + 1] / [-5sqrt(2) + 3]
To rationalize the denominator, we multiply top and bottom by the bottom's conjugate; that is, -5sqrt(2) - 3. Note that multiplying a binomial (a + b) by its conjugate (a - b) leads to a difference of squares; (a + b)(a - b) = a^2 - b^2. This is precisely what happens.
[2sqrt(2) + 1] [-5sqrt(2) - 3] / ( [-5sqrt(2)]^2 - 3^2 )
Note that squaring -5sqrt(2) leads to the product of squaring the (-5) and squaring the square root of 2. Remember that the square of a square root is itself.
[2sqrt(2) + 1] [-5sqrt(2) - 3] / [25(2) - 9]
Let's expand the top, and simplify the bottom.
[-10(2) - 6sqrt(2) - 5sqrt(2) - 3] / [50 - 9]
Some more simplification,
[-20 - 11sqrt(2) - 3] / 41
[-23 - 11sqrt(2)] / 41
2007-01-20 10:26:35
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answer #1
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answered by Puggy 7
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Hi, if the denominator contains a square root plus some other terms, a special trick does the job. It makes use of the difference of two squares formula:
(a + b)(a – b) = a^2 – b^2 ( equ. 1)
In your case we multiply with the factor (+5*sqrt(2) + 3)
(2*sqrt(2) + 1)*(+5*sqrt(2) + 3)/((-5*sqrt(2) + 3)*(+5*sqrt(2) + 3))
The denominator according to above stated trick equals
9 - 25*2 = -41
Therefore (2*sqrt(2) + 1)*(5*sqrt(2) + 3) =
10*2 + 6*sqrt(2) + 5*sqrt(2) + 3 =
23 + 11*sqrt(2)
This gives us the final simplification
-(23 + 11*sqrt(2))/41
2007-01-20 10:58:41
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answer #2
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answered by eschellmann2000 4
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[2sq rt(2) + 1] / [-5sq rt(2) + 3]
To rationalize the denominator, we multiply top and bottom by the bottom's conjugate; that is, -5sq rt(2) - 3. Note that multiplying a binomial (a + b) by its conjugate (a - b) leads to a difference of squares; (a + b)(a - b) = a^2 - b^2. This is precisely what happens.
[2sq rt(2) + 1] [-5sq rt(2) - 3] / ( [-5sq rt(2)]^2 - 3^2 )
Note that squaring -5sq rt(2) leads to the product of squaring the (-5) and squaring the square root of 2. Remember that the square of a square root is itself.
[2sq rt(2) + 1] [-5sq rt(2) - 3] / [25(2) - 9]
Let's expand the top, and simplify the bottom.
[-10(2) - 6sq rt(2) - 5sq rt(2) - 3] / [50 - 9]
Some more simplification,
[-20 - 11sq rt(2) - 3] / 41
[-23 - 11sq rt(2)] / 41
or in a more simplified answer:
What Puggy said....lol
2007-01-20 10:34:03
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answer #3
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answered by hambone65 2
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Do you mean > [2V`(2) + 1] / [- 5V`(2) + 3]?
First: multiply the conjugate of the denominator by the top & bottom which is, [- 5V`(2) - 3] (it has the opposite sign of addition > subtraction)...
[2V`(2) + 1]*[(- 5V`(2) - 3] / [- 5V`(2) + 3]*[- 5V`(2) - 3)]
Sec: use the foiling method for the top & bottom > let's "foil" the numerator...
[(2V`2)(-5V`2) + (2V`2)(-3) + (1)(-5V`2) + (1)(-3)]
[(-10V`4) - 6V`2 - 5V`2 - 3]
[(-10V`2*2) - 6V`2 - 5V`2 - 3]
[(-10)(2) - 6V`2 - 5V`2 - 3]
[-20 - 11V`(2) - 3]
[-23 - 11V`2]
*Let's "foil" the denominator...
[-5V`2 + 3]*[- 5V`2 - 3)]
[(-5V`2)(-5V`2) - (5V`2)(-3) + (3)(-5V`2) + (3)(-3)]
[(25V`(4) - (-15V`2) + (-15V`2) + - 9]
[(25V`(2*2) - (-15V`2) + (-15V`2) + - 9]
[(25(2) - (-15V`2) + (-15V`2) + - 9]
[50 + 15V`2 -15V`2 - 9]
[50 - 9] = 41
Third: place the new numerator over the denominator...
[-23 - 11V`2] / 41
2007-01-20 10:55:58
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answer #4
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answered by ♪♥Annie♥♪ 6
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only combine like-words Constants are for constants, variables are for variables... 2b+8-b+2 you will be able to desire to rearrange them so as which you will no longer get at a loss for words (2b - b) + (8 + 2) b + 10 ...........answer
2016-12-16 09:20:53
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answer #5
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answered by Anonymous
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