If you mean \(\sqrt{x-y}\), you cannot seperate \(x\) and \(y\) into \(\sqrt{x}-\sqrt{y}\). If \(x\) and \(y\) was \(\sqrt{x\times y}\), then you can seperate \(x\) and \(y\) into \(\sqrt{x}\times\sqrt{y}\). If \(x\) and \(y\) was \(\sqrt\frac{{x}}{y}\), then you an seperate \(x\) and \(y\) into \(\frac{{\sqrt x}}{\sqrt y}\). If you mean \(\sqrt{x}-y\), you cannot add a \(\sqrt{}\) to y, that would change the problem entirely.
Example:
Let \(x=3\) and let \(y=2\)
\(\sqrt{x-y}\)
\(\sqrt{3-2}\)
\(\sqrt{1}\)
\(1\)
The answer is \(1\)
Now lets do \(\sqrt{x}-\sqrt{y}\)
Let \(x=3\) and let \(y=2\)
\(\sqrt{x}-\sqrt{y}\)
\(\sqrt{3}-\sqrt{2}\)
\(1.7320508075688773...-1.414213562373095...\)
\(0.3178372451957823...\)
The answer is \(0.3178372451957823...\)
\(1\) and \(0.3178372451957823...\) are not the same answer.
Now lets do \(\sqrt{x\times y}\)
Let \(x=3\) and let \(y=2\)
\(\sqrt{x\times y}\)
\(\sqrt{3\times 2}\)
\(\sqrt{6}\)
\(2.4494897427831781...\)
The answer is \(2.4494897427831781...\)
Now lets do \(\sqrt{x}\times\sqrt{y}\)
Let \(x=3\) and let \(y=2\)
\(\sqrt{x}\times\sqrt{y}\)
\(\sqrt{3}\times\sqrt{2}\)
\(1.7320508075688773... \times 1.414213562373095...\)
\(2.4494897427831781...\)
The answer is \(2.4494897427831781...\)
\(2.4494897427831781...\) and \(2.4494897427831781...\) are the same answer.
Now lets do \(\sqrt\frac{{x}}{y}\)
Let \(x=3\) and let \(y=2\)
\(\sqrt\frac{{x}}{y}\)
\(\sqrt\frac{{3}}{2}\)
\(1.224744871391589...\)
The answer is \(1.224744871391589...\)
Now lets do \(\frac{{\sqrt x}}{\sqrt y}\)
Let \(x=3\) and let \(y=2\)
\(\frac{{\sqrt x}}{\sqrt y}\)
\(\frac{{\sqrt 3}}{\sqrt 2}\)
\(\frac{1.7320508075688773...}{1.414213562373095...}\)
\(1.224744871391589...\)
The answer is \(1.224744871391589...\)
\(1.224744871391589...\) and \(1.224744871391589...\) is the same answer
Now lets do \(\sqrt{x}-y\)
Let \(x=3\) and let \(y=2\)
\(\sqrt{x}-y\)
\(\sqrt{3}-2\)
\(1.7320508075688773...-2\)
\(-0.2679491924311227...\)
The answer is \(-0.2679491924311227...\)
Now let do \(\sqrt{x}-\sqrt y\)
Let \(x=3\) and let \(y=2\)
\(\sqrt{x}-\sqrt y\)
\(\sqrt{3}-\sqrt 2\)
\(1.7320508075688773...-1.414213562373095...\)
\(0.3178372451957823...\)
The answer is \(0.3178372451957823...\)
\(-0.2679491924311227...\) and \(0.3178372451957823...\) are not the same answer
Hope this helps
