Question

How do you get from this equation to this equation? Help me please?

Answer 1

You simplfiy it

Answer 2

when I do that I get \[+/-\sqrt{\frac{ 2+\sqrt{2} }{ 4}}\] but that isnt the right answer

Answer 3

$$\frac{\sqrt{2}}{2} = \frac{1}{\sqrt{2}}$$ because if you multiply both the numerator and denominator by \(\sqrt{2}\):
$$\frac{\sqrt{2} \cdot \sqrt{2}}{2 \cdot \sqrt{2}} = \frac{2}{2\sqrt{2}} = \frac{1}{\sqrt{2}}$$

Answer 4

so now we have
$$\frac{\sqrt{2+\frac{1}{\sqrt{2}}}}{\sqrt{2}}$$
so now we just multiply both the num. and denom of the whole thing by sqrt(2)...

Answer 5

But I thought you only rationalized to get the square-root out of the denominator?

Answer 6

well in the case of sqrt(2)/2 it's just to simplify it.
ignore my lack of latex for a second, but you can also expand 2 = sqrt(4) so that sqrt(2)/2 = sqrt(2)/sqrt(4) = sqrt(2/4) = sqrt(1/2) = 1/sqrt(2)

Answer 7

anyway, continuing on
$$\frac{\sqrt{2} \sqrt{2+\frac{1}{\sqrt{2}}}}{2} = \frac{\sqrt{2(2+\frac{1}{\sqrt{2}})}}{2} = \frac{\sqrt{4+\frac{2}{\sqrt{2}}}}{2}$$

Answer 8

can you simplify it from there?