Algebraic Brain Explosion

[Goldenboko]

So, I've got something I know will be included in a test tomorrow (the test isn't on it, but it's a little detail which will end up hurting me D: ).


Apparently fractions inside square roots are no-goes. So when you have something that looks like sqrt(1-sqrt(3)/2) you have to get rid of the two. My book ends up showing the answer as 1/2sqrt(2-sqrt(3)) Which confuses me, how did they simplify to get that?

If it helps here's the original question, "Use the half-angle formulas to determine the exact value of the sin 105 degrees".

[Jessweeee♪]

uhh...so is that one part sqrt³/₂ or sqrt3 divided by 2? It's so hard to read radicals this way ;_;

[Goldenboko]

Oh whoops.

sqrt((1-sqrt(3))/2)

[Flying Mullet]

See if this helps you write out your formulas:

1 - (√3)/2

[Jessweeee♪]

...I didn't think you could have a radical in a radical if you couldn't have a fraction in a radical, math is weeeird.

I got

(¹/₂)√(2-2√(3))



if that's what you meant to type in the first post then I can help, if not then I'm doing it wrong and will be useless xD

[Goldenboko]

Redid the problem, basic math error in the beginning screwed me later on. I'm good

[rubah]

you can have a fraction in a radical, jesse. you just rewrite it as the square root of the numerator divided by the square root of the denominator, like √(1/2) = √(1)/√(2) then you can multiply top and bottom by √(2) to get rid of the square root in the denominator, but it's completely useless and only jerkfaces make you do that.

for √(1-√(3)/2) you'd multiply the two terms inside the outer √ by two but you'd have to divide by √2 twice on the outside, so:

√((1*2) - 2√(3)/2)) * (1/√(2)) * (1/√(2))

so that simplifies to
√(2 - √(3)) * (1/√(2))²

the √ and ² cancel (square root is basically ^1/2 so you multiply them out to get 1) so you just get *(1/2)

[edit- grrrrrrrrrrrrrr gobo!]

[Rye]

I'm just squinting at this thread in confusion, trying to remember when I've learned this. I've taken up to Pre-Calc in math, so I must have, but jeez.

Oh well. I finished all of my math requirements in college, I never have to do any advanced math again! And my Science credit will be down after I take Bio, so I won't even need to solve Chem equations. YAY! ♥

Good luck!

[Jessweeee♪]

I hate chemistry equations. I hate them. My math and my science grades are always totally opposite for the same reason! Math!

[Aerith's Knight]

I always think: "Finally a math problem, not some kind of Japanese, post-modern American studies crap." but when I get there everything is already solved. ;_;

I HATE YOU! jk, just mildly despise

[rubah]

that's because we all think the same thing and hurry to beat each other to be the one to answer.

[Goldenboko]

I love asking the question and watching the ensuing dogfight =D

[Jessweeee♪]

We all gotta look smart, you know

[scrumpleberry]

Make a maths nerdery thread!

[Aerith's Knight]

Been there, done that.

Make a physics one instead.