Question # 01: Find the square root of the following polynomials by factorization method:
\((v)\) \(\; \) \(200t^2-120t+18\)
Solution:
$=200t^{2} -120t+18$
$=2\left[ 100t^{2} -60t+9\right]$
$=2\left[( 10t)^{2} -2( 10t)( 3) +3^{2}\right]$
$\displaystyle =2( 10t-3)^{2}$
Taking square root, we have
$ $$\sqrt{200t^{2} -120t+18} =\pm \sqrt{2( 10t-3)^{2}}$
$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =\pm \sqrt{2}( 10t-3)$