Question 1124474
<pre>
How would you simplify the equation:
Sqrt(17-12sqrt2) in the form
(a+bsqrt2)
Thank you. 
**********************************<font face = tahoma><font size = 2><font color = blue><b>
Not an equation, but an expression, instead!!
                           {{{sqrt(17 - 12sqrt(2))}}}
                    {{{sqrt(17 - 2(6)sqrt(2))}}} ----- Changing 12 to 2*6
                     {{{sqrt(17 - 2sqrt(36)sqrt(2))}}} ------ Converting 6 to {{{sqrt(36)}}}
                         {{{sqrt(17 - 2sqrt(72))}}} ------ Applying {{{sqrt(m)sqrt(n) = sqrt(mn)}}}
                  {{{sqrt(9 + 8 - 2(9*8))}}} ----- Changing 17 to 9 + 8, and 72 (in {{{sqrt(72)}}}) to 9*8
                    {{{sqrt(9 + 8 - 2sqrt(9)sqrt(8))}}} ------ Applying {{{sqrt(m*n) = sqrt(m)sqrt(n)}}}
  {{{sqrt((sqrt(9))^2 + (sqrt(8))^2 - 2sqrt(9)sqrt(8))}}} ------ Converting {{{system(matrix(2,3, 9, to, (sqrt(9))^2, 8, to, (sqrt(8))^2))}}}
The above is in the form: {{{(a - b)^2}}}, with {{{system(matrix(2,3, a, being, sqrt(9), b, being, sqrt(8)))}}}, and so:
{{{sqrt((sqrt(9))^2 + (sqrt(8))^2 - 2sqrt(9)sqrt(8))}}} then becomes: {{{sqrt((sqrt(9) - sqrt(8))^2)}}} 
                                                                                {{{sqrt(9) - sqrt(8)}}} ----- Cancelling SQUARE and SQUARE ROOT
                                                                                {{{highlight(3 - 2sqrt(2))}}}</font></font></font></b></pre>