Question 49473
Is the following a perfect square? {{{x^2+8x+81}}}

Quite likely! Notice that the first term is a perfect square {{{x^2 = (x)^2}}} and the last term is a perfect square {{{(9)^2 = 81}}} and the sum of 9+9 = 18 which is the coefficient of the x-term. So, if you factor the given expression, you'll get:
{{{(x+9)(x+9) = (x+9)^2}}} A perfect square!