How do you simplify √[14 + 8√[3]]?

Question

√means square root and the brackets are the stuff in them.

I am really confused and don't know where to start.

Answer 1

One of the ways is as following:

Under the square root we have 14+8√3=2(7+4√3)=

=2(4+2*2*√3+3)= 2(2²+2*2*√3+(√3)²) =

=|Here I use (a+b)²=a²+2ab+b²|=

= 2(2+√3)^2.

 

So 

√[14+8√[3]] = √[2(2+√3)² ]=(2+√3)√2.

 

or you can write as

√8+√6

This expression is relatively simple but it still could be done more simpler (if you want)

If questions, let me know.

 

Answer 2

If

√(14 + 8√3) I do not know of a simiplification