## Precalculus: Mathematics for Calculus, 7th Edition

$a)$ $9\sqrt{x^{2}+1}$ $b)$ $6\sqrt{x^{2}+y^{2}}$
$a)$ $\sqrt{81x^{2}+81}$ 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: $...=(\sqrt{36})(\sqrt{x^{2}+y^{2}})=6\sqrt{x^{2}+y^{2}}$