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# Help

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does √x-y = √x-√y

Jan 12, 2016

#2
+5

√x-y = √x-√y   (???)    square both sides

x - y = x - 2√[x *y]  + y    subtract x from both sides  and rearrange

2√[x *y]  = 2y        divide both sides by 2

√[x * y]  = y

√x * √y  = y

√x * √y  - y  =  0        factor

√y [ √x  - √y]  = 0

So either    √y  = 0      or    √x  = √y

So....the original equation is true only when x = y   or    y = 0   Jan 12, 2016

#1
+5

NOOOOOO

You can't

it works for multiplcation or division

Jan 12, 2016
#2
+5

√x-y = √x-√y   (???)    square both sides

x - y = x - 2√[x *y]  + y    subtract x from both sides  and rearrange

2√[x *y]  = 2y        divide both sides by 2

√[x * y]  = y

√x * √y  = y

√x * √y  - y  =  0        factor

√y [ √x  - √y]  = 0

So either    √y  = 0      or    √x  = √y

So....the original equation is true only when x = y   or    y = 0   CPhill Jan 12, 2016
#3
+5

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

Jan 12, 2016