解：$(1) \sqrt {4+\frac 4{15}}=4 \sqrt {\frac 4{15}} $
验证：$ \sqrt {4+\frac 4{15}}=\sqrt {\frac {64}{15}}=\sqrt {\frac {4^2 ×4}{15}}=4 \sqrt {\frac 4{15}}$
$ (2) \sqrt {a+\frac a{a^2-1}}=a \sqrt {\frac a{a^2-1}} $
证明：$ \sqrt {a+\frac a{a^2-1}}=\sqrt {\frac {a^3}{a^2-1}}=a \sqrt {\frac a{a^2-1}} $
