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Write in simplified radical form by rationalizing the denominator:

(2 * sqrt(2)+1)/(-5*sqrt(2)+3)

2007-01-20 10:16:58 · 5 answers · asked by Chazzy 3 in Science & Mathematics Mathematics

5 answers

[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 · answer #1 · answered by Puggy 7 · 0 0

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 · answer #2 · answered by eschellmann2000 4 · 0 0

[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 · answer #3 · answered by hambone65 2 · 0 1

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 · answer #4 · answered by ♪♥Annie♥♪ 6 · 0 0

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 · answer #5 · answered by Anonymous · 0 0

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