Write your answer in simplest Simplify: sqrt(2009*2011*2015*2017+36)+10. Write your answer in simplest form


Let $\displaystyle\frac{2009+2011+2015+2017}4=2013=a$
$\displaystyle\implies 2009\cdot2011\cdot2015\cdot2017=(a-4)(a-2)(a+2)(a+4)$
$\displaystyle=(a^2-16)(a^2-4)=a^4-20a^2+64$
Now, $\displaystyle 2009\cdot2011\cdot2015\cdot2017+36$
$\displaystyle=a^4-20a^2+64+36=(a^2)^2+10^2-2\cdot a^2\cdot10=(a^2-10)^2$
