my question is this : Why is the sqrt[(2+sqrt(3))/4] = sqrt[2+sqrt(3)]/4 ?

I thought it would be equal to sqrt[2+sqrt(3)]/2 but I saw the real answer. What am I doing wrong ? (im just taking the squareroot of the denominator. am I not supposed to do that?

2. Originally Posted by frankinaround
my question is this : Why is the sqrt[(2+sqrt(3))/4] = sqrt[2+sqrt(3)]/4 ?

I thought it would be equal to sqrt[2+sqrt(3)]/2 but I saw the real answer. What am I doing wrong ? (im just taking the squareroot of the denominator. am I not supposed to do that?
$\displaystyle\frac{\sqrt{2+\sqrt{3}}}{\sqrt{4}}=\f rac{\sqrt{2+\sqrt{3}}}{\pm 2}$

Who said it was

$\displaystyle\frac{\sqrt{2+\sqrt{3}}}{4}\text{?}$

3. In short, it's not.

$\displaystyle \sqrt{\frac{2 + \sqrt{3}}{4}} = \frac{\sqrt{2 + \sqrt{3}}}{\sqrt{4}} = \frac{\sqrt{2 + \sqrt{3}}}{2} \neq \frac{\sqrt{2 + \sqrt{3}}}{4}$.

4. Originally Posted by frankinaround
my question is this : Why is the sqrt[(2+sqrt(3))/4] = sqrt[2+sqrt(3)]/4 ?
For the same reason 2 is equal to 4!!

[I thought it would be equal to sqrt[2+sqrt(3)]/2 but I saw the real answer. What am I doing wrong ? (im just taking the squareroot of the denominator. am I not supposed to do that?