Can someone help me with conjugates in algebra i will fan and medal

Question

otakulyfe · Answer

attachment

otakulyfe · Answer

@zarkam21

thomas123 · Answer

...

thomas123 · Answer

what grade level?

otakulyfe · Answer

sophmore algebra

thomas123 · Answer

hmmm What is the question?

otakulyfe · Answer

its posted at the top i attached a picture of the equation

rsadhvika · Answer

Conjugate of $\sqrt{a} \color{red}{-}\sqrt{b}$ is  $\sqrt{a} \color{red}{+} \sqrt{b}$

otakulyfe · Answer

yes i know the conjugates rule of reversing the sign

rsadhvika · Answer

Look at the bottom of given fraction.
Can you find its conjugate ?

otakulyfe · Answer

$$\sqrt{5+\sqrt{3}}$$

otakulyfe · Answer

$$\sqrt{5} + \sqrt{3}$$

rsadhvika · Answer

Yes multiply that top and bottom so that the bottom becomes nice looking

rsadhvika · Answer

Recall the identity $$(a-b)(a+b)=a^2-b^2$$

otakulyfe · Answer

$$\left( \sqrt{6} \left( \sqrt{5} + \sqrt{3} \right) \right)$$

rsadhvika · Answer

$$\dfrac{ \sqrt{6}\color{red}{ \left( \sqrt{5} + \sqrt{3} \right)} }{\color{red}{\color{black}{ \left( \sqrt{5} - \sqrt{3} \right)} \left( \sqrt{5} + \sqrt{3} \right)}}$$

rsadhvika · Answer

$$\dfrac{ \sqrt{6}\color{red}{ \left( \sqrt{5} + \sqrt{3} \right)} }{5-3}$$

rsadhvika · Answer

Does that simplify to
$$\dfrac{\sqrt{30}}{2} + \dfrac{3\sqrt{2}}{2}$$

?

otakulyfe · Answer

yes

otakulyfe · Answer

is anyone even helping me at this point

dumbcow · Answer

looks like all the work is done :)
@rsadhvika provided final  answer

otakulyfe · Answer

oh dang he did