SOLUTION: How do you deal with square roots within square roots, for example sqrt(4 + 2sqrt3)/sqrt2? Thank you for your help!

Question 87556: How do you deal with square roots within square roots, for example
sqrt(4 + 2sqrt3)/sqrt2?
Thank you for your help!
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
It doesn't happen very often, but let's try it. Just remember to obey the rules, and don't make up new rules that aren't true for all real numbers. What we know is that you can multiply provided a and b are NOT both negative. Also, you know that rationalizing the denominator is always a good place to start:

Now, be really careful not to change the rules or make up "new" ones!

Now, I know this is correct because I checked it with my calculator. However, there may be something else that can be done to eliminate the square root of the square root. I remember doing something like this about 20 years ago in trigonometry, but I haven't worked with it in a very long time. Therefore, if you want a second opinion, go ahead and post the question again, and see if someone else has some ideas about it.

This is a very interesting problem!!

R^2 Retired from SCC

RELATED QUESTIONS
how do you do square roots? for example... (answered by jim_thompson5910,stanbon,shree840)

How do you solve and simplify square roots? For example the square root of... (answered by ReadingBoosters,DrBeeee)

hello, i already did this problem but i feel like its wrong so can you please check it (answered by Alan3354)

how do you add square roots? example: square root of 18 + the square root of... (answered by ewatrrr)

Can you please explain how to multiply square roots? For example,... (answered by stanbon,lwsshak3)

multiply (5sqrt3 - 15sqrt7)(2sqrt3 +6sqrt7)= Thank you for your... (answered by checkley77)

can you help me with square... (answered by solver91311)

How do you simplify square... (answered by stanbon)

How do you add square roots? sqrt of x+3 + sqrt of 6-x ? (answered by fcabanski)