simplify √(23+√408) -√(23-√408) ?

Answer 1

LOL

a^2 - b^2 = (a+b)(a-b)
so
23 - 408 = (sqrt(23) -sqrt....

Answer 2

Let 23=x
408=y
N= final answer

then

√(23+√408) - √(23-√408) becomes

√(x+√y) - √(x-√y)

Equating it to N

√(x+√y) - √(x-√y)=N

Solving this,

N²= 2x-2√(x²-y)

Subsituting x=23 and y=408

N²=2(23)-2√(23²-408)
=46-2√(529-408)
=46-2√121
=46-2(11)
=46-22
=24

N²=24
N=2√6.

I hope it helps.