Question

How do you simplify `sqrt(x^2+y^2)`?

Answer 1

You can't, really.

Explanation:

While it looks like you can just cancel out the squares with the square root, this only works if you have one square within the radical. Since we're adding two together, it's slightly different.

There's no way to factor `x^2+y^2` to get a perfect square.

The only real way to simplify this expression is by using math that's at a higher than algebra level, so for all intents and purposes, `sqrt(x^2+y^2)` is about as simple as you can get.

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Note:

The way that this expression CAN be simplified is by using polar coordinates, which are found in pre-calculus and above.

One of the conversion formulas for rectangular to polar coordinates is:

`x^2+y^2 = r^2`

Therefore, if we assume that the `x` and `y` this problem is using are the horizontal and vertical directions on a coordinate plane, we could technically rewrite our expression as:

`sqrt(x^2+y^2)`

`sqrt(r^2)`

`r`

Remember, this is probably NOT what your teacher is looking for, unless you're in pre-calculus or above. I would just stick with the original answer that the expression cannot be simplified.