# Simplify (30-x^2)^1/2

1. Apr 13, 2010

### 0tt0UK

Hi all,

I found this (30-x2)1/2

Would it be the same as (sqrt30 - x) ??

Is there any way to simplify it?

2. Apr 13, 2010

### sylas

You cannot simplify it any further. You cannot distribute the square root over the addition.

3. Apr 13, 2010

### 0tt0UK

thx sylas that is what I thought but I wasn't sure..

so if I had to multiply that by lets say (2+x). What would happen to the square root (1/2)?

Add the exponents due to the multiplication (1 + 1/2 = 3/2)?

4. Apr 13, 2010

### Mentallic

So you will have $$(2+x)\sqrt{30-x^2}$$ ??
Nothing happens to the square root :tongue:

Oh and by the way, the rule is $$\sqrt{a^2}=a$$ for a being anything, simple or complicated. Think a bit about this rule and see if you can figure out why you can't simplify the above expression.

5. Apr 13, 2010

### 0tt0UK

Yes I understand that, ta.

But what would be the multipication between both? That is what I don't get..

6. Apr 13, 2010

### Mentallic

Think about this, $$(a+b)^2=?$$

7. Apr 13, 2010

### D H

Staff Emeritus
The rule is $$\sqrt{a^2} = |a|$$, not $$\sqrt{a^2}=a$$, and even that rule applies for the real numbers only.

8. Apr 13, 2010

### 0tt0UK

(a+b)^2 = (a+b)(a+b)

9. Apr 13, 2010

### Mentallic

lol ok I wasn't expecting that answer. Expand it!!

10. Apr 13, 2010

### Mentallic

DH let's not get picky now, are you trying to confuse him?

Oh and p.s. what I meant by complicated was that $a$ could be a function of anything more complicated, such as $\sqrt{30}-x$ for example
(not complex numbers)...

11. Apr 13, 2010

### 0tt0UK

$$(a+b)^2$$ is ok but what to do when the exponent is square root ?

That is what I don't get, the expansion!

$$(2+x)\sqrt{30-x^2}$$

12. Apr 13, 2010

### Staff: Mentor

I'm with D H that $$\sqrt{x^2} = |x|$$
Consider $$\sqrt{(-3)^2} = \sqrt{9} = 3 = |-3|$$
It might be that a slight complication in pursuit of the truth can be confusing, but telling a student a rule that is incorrect is worse than confusing.

13. Apr 13, 2010

### sylas

There's nothing you can do. (a+b)0.5 cannot be simplified further.

That isn't an expansion. It's just writing (30-x2)0.5 using a square root sign instead of the exponent.

Cheers -- sylas

14. Apr 13, 2010

### 0tt0UK

thx sylas.. what would you get when multiplying (30-x2)0.5 by (2+x) or any (a+b)?

An exponent, it would be ok. I cannot do it with the square root.

15. Apr 13, 2010

### sylas

You can't simply the multiplication either. The expressions you describe are:
\begin{align*} (2+x)(30-x^2)^{0.5} \\ (a+b)(30-x^2)^{0.5} \end{align*}​
Neither of those expressions can be simplified.

16. Apr 13, 2010

### 0tt0UK

ooh.. ok! thank you all for your help

17. Apr 13, 2010

### Mentallic

I was trying to give 0tt0UK an understanding of why this cannot be simplified to $$\sqrt{30}-x$$ !!

Seriously.... have you guys not figured out yet what 0tt0UK's mathematical level is? He's learning about pythagoras' theorem for Christ sake! What is the point of saying "oh, but $$\sqrt{a^2}=|a|$$ since... wait, you don't understand why this is true? *goes off on a massive tangent to explain something that is unnecessary for 0tt0UK's case*... but really, this won't be happening in Pythagoras' theorem because side lengths in triangles are positive... not negative, and not complex".
He has no need to learn the refined rule. It's just the same reason why a teacher would never even dare to explain to their students why such a rule doesn't work for complex numbers, since they've never heard about them before, and it would drag the lesson in the wrong direction. 0tt0UK can come back to the proper rule when necessary. Not now.

That's not what I was trying to get at :tongue:
I'm trying to shed some light on why $$\sqrt{30-x^2}\neq \sqrt{30}-x$$

Think about this, in the rule $$\sqrt{a^2}=a$$ (where a is a length... thus, positive)
what about if we substituted a=x+y ? Then we'll have $$\sqrt{(x+y)^2}=x+y$$

But expand the $$(x+y)^2$$ and see if you notice something. Now do the same for $$(\sqrt{30}-x)^2$$ and see what you get.