## Algebra and Trigonometry 10th Edition

The given operation is not valid: $\sqrt {5u}+\sqrt {3u}=\sqrt {5u+3u}$ If it were: $\sqrt {5u+3u}=\sqrt {8u}=\sqrt {2^2(2u)}=2\sqrt {2u}$
Square both sides: $(\sqrt {5u}+\sqrt {3u})^2\ne(2\sqrt {2u})^2$ $(\sqrt {5u})^2+2\sqrt {5u}\sqrt {3u}+(\sqrt {3u})^2\ne2^2(\sqrt {2u})^2$ $5u+2\sqrt {(5u)(3u)}+3u\ne4(2u)$ $8u+\sqrt {15u^2}\ne8u$ $8u+\sqrt {15}u\ne8u$ Now, it's clear why $\sqrt {5u}+\sqrt {3u}\ne2\sqrt {2u}$