Question

What is the simplified form of this expression sqaure root 8x^3+24x^2+18x? a ±(2x + 3) b ±(4x + 6) c ±(2x + 3) d ±(4x + 6)

Answer 1

`\bf √(8x^3+24x^2+18x)\implies √(2x(4x^2+12x+9)) \\\\\\ \textit{now, let's check } \begin{cases} 4x^2=2^2x^2\\ \qquad (2x)^2\\ 9=3^2\\ 12x=2(2x)(3) \end{cases}\impliedby \textit{a perfect square trinomial} \\\\\\ \sqrt{2x[(\underline{2x})^2+2(\underline{2x})(\underline{3})+\underline{3}^2]}\implies √(2x(2x+3)^2) \\\\\\ \boxed{\pm (2x+3)√(2x)}`