\( \Large \frac{ \left(x^{2}+2x-1\right) \left(x^{2}+2x+1\right) + 1 }{x^{2}+2x+1} \) =\( \Large \frac{\left(x^{2}+2x\right)^{2}-1+1}{ \left(x+1\right)^{2} } = \left(\frac{x^{2}+2x}{x+1}\right)^{2} \) Hence required positive square root =\( \Large \frac{x^{2}+2x}{x+1}=\frac{x^{2}+2x+1 - 1}{ \left(x+1\right) } \) =\( \Large \frac{ \left(x+1\right)^{2}-1 }{ \left(x+1\right) } = \left(x+1\right)-\frac{1}{ \left(x+1\right) } \)
\( \Large 9^{60}= \left(3^{2}\right)^{60}=3^{120} \) and \( \Large 27^{35}= \left(3^{3}\right)^{35}=3^{105} \)
\( \Large 9^{60} > 27^{35} \)