1. Apr 22, 2015

### Emmanuel_Euler

hi guys
i know all square root and any root(cubic......) rules

sqrt(x)=x^(1/2)
sqrt(x^2)=abs(x)
sqrt(xy)=sqrt(x)*sqrt(y)
sqrt(x/y)=sqrt(x)/sqrt(y)
sqrt(-x)=isqrt(x)
f'(x)=1/2sqrt(x)
F(x)=2/3*(x^3/2)
..............
my question is:
is there any rules for this sqrt(x+y)
or sqrd(x-y)??

2. Apr 22, 2015

### HallsofIvy

Staff Emeritus
No, there is no way to simplify a square root (or other root) of a sum or difference.

It's simply a case of "multiplication and addition do not play well together!"

3. Apr 22, 2015

### Emmanuel_Euler

Yes of course.
you are right there is no rule for this sqrt(x+y)
thanks for help friend.

4. Apr 22, 2015

### Staff: Mentor

You should be aware that there are restrictions on x and y; namely, both must be nonnegative. I.e., x ≥ 0 and y ≥ 0. Without these restrictions you get nonsense like $1 = \sqrt{1} = \sqrt{-1 * -1} = \sqrt{-1} * \sqrt{-1} = i * i = -1$
There are restrictions here, as well, with x ≥ 0 and y > 0.
Not true. For example, if x = -4, then $\sqrt{-(-4)} = \sqrt{4} = 2$. $i\sqrt{-4} = i * (2i) = 2i^2 = -2$.
Here you seem to be tacitly assuming that -x will be negative, which is not true in general.

5. Apr 22, 2015

### Emmanuel_Euler

Friend:i know all the rules you wrote.
i was too busy to write them all(in my question).
But if you really want to help me,find a rule for this sqrt(x+y).

6. Apr 22, 2015

### Emmanuel_Euler

Forgive me!, i was busy and hurry.

7. Apr 22, 2015

### Staff: Mentor

There is no such rule.

Period.

8. Apr 22, 2015

### Emmanuel_Euler

You are right.

9. Apr 24, 2015

### micromass

Staff Emeritus
10. Apr 25, 2015

### Emmanuel_Euler

That helps.
thank you for help,i will read it later!!