Answer
$a)$ $9\sqrt{x^{2}+1}$
$b)$ $6\sqrt{x^{2}+y^{2}}$
Work Step by Step
$a)$ $\sqrt{81x^{2}+81}$
Take out common factor $81$ from the expression inside the square root:
$\sqrt{81x^{2}+81}=\sqrt{81(x^{2}+1)}=...$
Take the square root of each factor:
$...=(\sqrt{81})(\sqrt{x^{2}+1})=9\sqrt{x^{2}+1}$
$b)$ $\sqrt{36x^{2}+36y^{2}}$
Take out common factor $36$ from the expression inside the square root:
$\sqrt{36x^{2}+36y^{2}}=\sqrt{36(x^{2}+y^{2})}=...$
Taka the square root of each factor:
$...=(\sqrt{36})(\sqrt{x^{2}+y^{2}})=6\sqrt{x^{2}+y^{2}}$
