Given:
The expression is,
[tex]-2\sqrt[]{24y^2}+5\sqrt[]{96y^2}[/tex]The objective is to simplify the expression.
The expression can be simplified as,
[tex]\begin{gathered} =-2\sqrt[]{2\times2\times2\times3\times y\times y}+5\sqrt[]{3\times2\times2\times2\times2\times2\times y\times y} \\ =-2(2)(y)\sqrt[]{2\times3}+5(2)(2)(y)\sqrt[]{2\times3} \\ =-4\sqrt[]{6}y+20\sqrt[]{6}y \\ =16\sqrt[]{6}y \end{gathered}[/tex]Hence, the simplified expression is 16(√6)y.
