Question # 01: Find the square root of the following polynomials by factorization method:
\((ii)\) \(\;\) \(9x^2+12x+4\)
Solution:
$=9x^{2} +12x+4$
$=( 3x)^{2} +2( 3x)( 2) +2^{2}$
$\displaystyle =( 3x+2)^{2}$
Taking square root, we have
$ $$\sqrt{9x^{2} +12x+4} =\pm \sqrt{( 3x+2)^{2}}$
$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =\pm ( 3x+2)$
——– Alternate Method ——–
$9x^{2} +12x+4$
$=9x^{2} +12x+4$
$=9x^{2} +6x+6x+4$
$=3x( 3x+2) +2( 3x+4)$
$=( 3x+2)( 3x+2)$
$\displaystyle =( 3x+2)^{2}$
Taking square root, we have
$ $$\sqrt{9x^{2} +12x+4} =\pm \sqrt{( 3x+2)^{2}}$
$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =\pm ( 3x+2)$