# Question on Laws of Exponents

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• Feb 25th 2011, 07:06 AM
Substince
Question on Laws of Exponents
Ok I'm at the end of my lesson and I have to prove if an expression is true or false.

eg: $(x+y)^{1/2} = x^{1/2}+y^{1/2}$

I know if it were $(xy)^{1/2}$ this would be equal to $x^{1/2}y^{1/2}$ but the addition sign is throwing me off.

I've looked at my rules and can't find anything like $(x+y)^2$ laws just the power of the product.

I hope I'm making sense :P

Thanks
• Feb 25th 2011, 07:14 AM
Prove It
It's not true. You can check using the Binomial Series...
• Feb 25th 2011, 07:16 AM
earboth
Quote:

Originally Posted by Substince
Ok I'm at the end of my lesson and I have to prove if an expression is true or false.

eg: $(x+y)^{1/2} = x^{1/2}+y^{1/2}$

I know if it were $(xy)^{1/2}$ this would be equal to $x^{1/2}y^{1/2}$ but the addition sign is throwing me off.

I've looked at my rules and can't find anything like $(x+y)^2$ laws just the power of the product.

I hope I'm making sense :P

Thanks

1. Re-write the expression as:

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

2. Square both sides and you'll see that this equation is only true if x = 0 or y = 0
• Feb 25th 2011, 07:19 AM
Substince
wonderful thank you guys!