Question

In the following exercises, simplify.$3\sqrt{75y^2}+8y\sqrt{48}-\sqrt{300y^2}$

Short answer

On simplification, we get$37y\sqrt{3}$

Step-by-step solution

Given information

Given the expression ,$3\sqrt{75y^2}+8y\sqrt{48}-\sqrt{300y^2}$

Simplifying the radical and combine like terms

Simplifying like terms, we get

$$\begin{gathered} 3\sqrt{75y^2}+8y\sqrt{48}-\sqrt{300y^2}=3\sqrt{25\times 3y^2}+8y\sqrt{16\times 3}-\sqrt{100\times 3y^2} \\ 3\sqrt{75y^2}+8y\sqrt{48}-\sqrt{300y^2}=3·5y\sqrt{3}+8y·4\sqrt{3}-10y\sqrt{3} \\ 3\sqrt{75y^2}+8y\sqrt{48}-\sqrt{300y^2}=15y\sqrt{3}+32y\sqrt{3}-10y\sqrt{3} \\ 3\sqrt{75y^2}+8y\sqrt{48}-\sqrt{300y^2}=37y\sqrt{3} \end{gathered}$$