Roots Problem!

**Astar** · March 12th 2011, 10:31 PM

You know those times when your doing maths and then for some reason you just CANNOT work out why a particular mathematical situation is that way! Well I just did.

FOr the life of me I cannot work out why the following happens:

How come

$\sqrt {x^2+y^2}\not= x + y$

Here is my thinking here.

$ \sqrt {x^2+y^2} = \sqrt {x^2} + \sqrt {y^2} = x + y $

Please help me out. Because I just have no idea.

**Prove It** · March 12th 2011, 10:35 PM

What is $\displaystyle (x + y)^2$ when expanded?

**mr fantastic** · March 12th 2011, 11:08 PM

Originally Posted by Astar

You know those times when your doing maths and then for some reason you just CANNOT work out why a particular mathematical situation is that way! Well I just did.

FOr the life of me I cannot work out why the following happens:

How come

$\sqrt {x^2+y^2}\not= x + y$

Here is my thinking here.

$ \sqrt {x^2+y^2} = \sqrt {x^2} + \sqrt {y^2} = x + y $

Please help me out. Because I just have no idea.

So you would have $\sqrt{1^2 + 1^2} = 1 + 1$ ....??!!

**Astar** · March 12th 2011, 11:14 PM

Originally Posted by Prove It

What is $\displaystyle (x + y)^2$ when expanded?

It equals $x^2 + 2xy + y^2$

So therefore you can say that:

$x+y = \sqrt{(x+y)^2}$

Then what does $\sqrt{x^2+y^2}$ equal then???

**CaptainBlack** · March 12th 2011, 11:19 PM

Originally Posted by Astar

It equals $x^2 + 2xy + y^2$

So therefore you can say that:

$x+y = \sqrt{(x+y)^2}$

Then what does $\sqrt{x^2+y^2}$ equal then???

There is no general further simplification

CB

**iBurger** · March 13th 2011, 03:26 AM

Originally Posted by Astar

...
Then what does $\sqrt{x^2+y^2}$ equal then???
...

I think it helps to read $\sqrt{x^2+y^2} = (x^2+y^2)^{.5} = (constant)^{.5}$

What you want to do,

$ \sqrt {x^2+y^2} = \sqrt {x^2} + \sqrt {y^2} = x + y $

Would be almost correct if it was $\sqrt {x^2*y^2}$ instead of $\sqrt {x^2+y^2}.$

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