Question

\(\sqrt{x}=15\)  

\(2\sqrt{x}=14\)

\(\sqrt{x}< \sqrt{2}\)

\(\sqrt{2x}< 4\)

Answer 1

a) \(\sqrt{x}=15\Rightarrow\left\{{}\begin{matrix}x\ge0\\x=15^2\end{matrix}\right.\Rightarrow x=225\)

b) \(2\sqrt{x}=14\Rightarrow\sqrt{x}=7\Rightarrow\left\{{}\begin{matrix}x\ge0\\x=7^2\end{matrix}\right.\Rightarrow x=49\)

c) \(\sqrt{x}< \sqrt{2}\Rightarrow\left\{{}\begin{matrix}x\ge0\\x< 2\end{matrix}\right.\Rightarrow0\le x< 2\)

d) \(\sqrt{2x}< 4\Rightarrow\left\{{}\begin{matrix}x\ge0\\2x< 16\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x\ge0\\x< 8\end{matrix}\right.\Rightarrow0\le x< 8\)