Question # 01: Find the square root of the following polynomials by factorization method:
\((iii)\) \(\;\) \(36a^2+84a+49 \)
Solution:
$36a^{2} +84a+49$
$=36a^{2} +84a+49$
$=( 6a)^{2} +2( 6a)( 7) +7^{2}$
$\displaystyle =( 6a+7)^{2}$
Taking square root, we have
$ $$\sqrt{36a^{2} +84a+49} =\pm \sqrt{( 6a+7)^{2}}$
$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =\pm ( 6a+7)$