Question 245988
When you factor {{{4x^4 + 36x^2 + 81}}} you find that it =
{{{(2x^2 + 9)(2x^2+9)}}}
.
To check, multiply through:
{{{2x^2*2x^2 + 2x^2*9 + 9*2x^2 + 9*9}}} =
{{{4x^4 + 18x^2 + 18x^2 + 81}}}
{{{4x^4 + 36x^2 + 81}}}.
We observe that:
{{{(2x^2 + 9)(2x^2+9)}}} is equivalent to:
{{{(2x^2 + 9)^2}}}
.
So, {{{sqrt(2x^2 + 9)^2)}}} equals:
{{{2x^2 + 9}}}
.
Note:  I had to assume the original equation is as I wrote it, which has a {{{36x^2}}} in the middle, not {{{36x}}}.