This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
4 solutions
the answer comes to 4, then why are we finding its square root??
Log in to reply
@Samriddhi Singha Roy The square of the expression comes out to be 4 ,so in order to find the value of the original expression,we have to find its square root.
this is wrong or maybe i didnt get it, but when i used a calculator i get 2.19275263435
Log in to reply
you must have done some thing wrong. my calculator gives me 2
XD I'm in yr 9 and not good at simplifying so it was pretty much a half guess for me and my working out was as simple as...
Since you can change
\sqrt{2} + \sqrt{6}
into
\sqrt{2 + 6}
You can change
\sqrt{2 + \sqrt{3}}
into
\sqrt{2} + \sqrt{3}
making it possible to write it as:
\frac {\sqrt{2} + \sqrt{6}} {\sqrt{2} + \sqrt{3}}
And so the
\sqrt {2}
cancel out and
\frac {\sqrt {6}} {/sqrt {3}}
= 2
P.S I'm new to this website and in the preview the symbols aren't working and I don't know why so hope you can understand if this fails :P
Log in to reply
you can't write it that way!
Let 2 + 3 2 + 6 = x squaring both sides 2 + 3 2 + 2 × 2 × 6 + 6 = x 2 2 + 3 4 ( 2 + 3 ) = x 2 x 2 = 4 x = 2 since x is positive
sqrt( 2 ) + sqrt( 6 ) = sqrt( 8 + 2 sqrt( 12 ) ) = sqrt( 8 + 4 sqrt( 3 ) ) = 2 sqrt( 2 + sqrt( 3 ) )
Hence ( sqrt( 2 ) + sqrt( 6 ) ) / sqrt( 2 + sqrt( 3 ) ) = 2
You cant cross out things that aren't being multiplied
If we square the expression, we get 2 + 3 2 + 2 2 ⋅ 6 + 6 = 2 + 3 8 + 4 3 = 4 , So, since the expression is positive, it must equal 4 = 2 .