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# Complex Square Root Fraction Simplification

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In a Trig book i'm studying it gives this fraction (the bottom one here). So the 2 divided by 2 was originally a 1 so i take it they used the 2 over 2 so they could get a suitable LCD to simplify the sum. Anyway the next step after this has the top sum pictured below with the 4 in the denominator.  Sorry for the way the sum is written the bottom one is the first and the top is the simplified version. So this will be easy for you guys but where is the 4 in the denominator coming from?  Is it just through multiplying everything through by 4 as the LCD?  Could someone write out the steps so i can visualise it?  Complex fractions are hard!

$$2- \sqrt{3}\over4$$

$$2/2 - \sqrt{3}\over2$$

MrSilvers  Apr 19, 2017

#3
+75302
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MrSilvers.......are you trying to take the half-angle of something?? Maybe trying to evaluate the sine of (15°) ??

If so.....we have

sin (15°)   =  √ [ (1 - √3/2) / 2 ]  =   √ [ (2/2 - √3/2) / 2 ]   =  √ [ (2 - √3) / 4]  =

√ (2 - √3) / 2

CPhill  Apr 19, 2017
edited by CPhill  Apr 19, 2017
edited by CPhill  Apr 19, 2017
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#1
+4154
+2

Hmm...that's funny....

So according to the book:    $$\frac{2/2-\sqrt3}{2}=\frac{2-\sqrt3}{4}$$   ???

As far as I can tell, those two are not equal.

$$\frac{2/2-\sqrt3}{2} \approx -0.366 \\~\\ \frac{2-\sqrt3}{4} \approx 0.067$$

I'm sorry...I don't know!

hectictar  Apr 19, 2017
#2
+27
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Sorry hectictar it's the way i wrote it out, it's wrong. It should be a square root then under the square root is 2/2 - sq root of 3/2 that's all in the numerator of the fraction. Then the 2 is in the denominator. That simplifies to the second sum i wrote but the second sum also is under a sq root. I omitted both of those roots in my post.  It's hard to write it out on here. Does that make more sense now? Sorry.

MrSilvers  Apr 19, 2017
edited by MrSilvers  Apr 19, 2017
#3
+75302
+2

MrSilvers.......are you trying to take the half-angle of something?? Maybe trying to evaluate the sine of (15°) ??

If so.....we have

sin (15°)   =  √ [ (1 - √3/2) / 2 ]  =   √ [ (2/2 - √3/2) / 2 ]   =  √ [ (2 - √3) / 4]  =

√ (2 - √3) / 2

CPhill  Apr 19, 2017
edited by CPhill  Apr 19, 2017
edited by CPhill  Apr 19, 2017
#4
+27
+1

Yes that's it. It's in the half angle section of the book. It's trig for dummies by Mary Jane Sterling. I just wondered about the breakdown of the simplified sum with the 4 in the denominator and whether the 4 came from using it as an LCD.

MrSilvers  Apr 19, 2017

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