Question 83552
 Simplify (rationalize all denominators) 
3/[SQRT(5) - 2] 
I am pretty sure I need to multiply 3/[SQRT(5) - 2] by SQRT(5)+2 / SQRT (5) +2.
Which I think would bring me to an answer of 3[SQRT(5)+6. I am not sure if i did everything right and am wonder if I came to the correct answer. Thank you.
<pre><b>
 
The other tutor saw your 3[SQRT(5)+6 and thought you meant 3[SQRT(5)+6] which
would have been wrong.  However you meant 3×SQRT(5)+6.  So I think you were
right.  Here, let's go through it and see:

{{{3/(sqrt(5)-2)}}} 

Multiply by

{{{ (sqrt(5)+2)/(sqrt(5)+2)}}}

{{{3/(sqrt(5)-2)}}}×{{{ (sqrt(5)+2)/(sqrt(5)+2)}}}

{{{( 3(sqrt(5)+2) )/( sqrt(5)+2 )(sqrt(5)-2)}}}  

Multiply the top out and FOIL out the bottom:

{{{( 3*sqrt(5)+6 )/(5-2*sqrt(5)+2*sqrt(5)-4)}}} 

The middle two terms in the bottom cancel, so we have

{{{( 3*sqrt(5)+6 )/(5-4)}}} 

{{{( 3*sqrt(5)+6 )/1}}}

{{{ 3*sqrt(5)+6 }}}

Looks like you're right!

Edwin</pre>