under a square root

**am1** · December 8th 2009, 08:45 PM

if i had squareroot(4+x^2) why can't i simplify it down to (2+x), why isn't that legal?

**bigwave** · December 8th 2009, 08:54 PM

Originally Posted by am1

if i had squareroot(4+x^2) why can't i simplify it down to (2+x), why isn't that legal?

$\sqrt{4+x^2}$ is the same as $\left(4 + x^2\right)^{\frac{1}{2}}$

the law is $(xy)^a = x^2y^a$

$(x + y)^a \ (x+y)$ has to be mulitplied by itself $a$ times

**am1** · December 8th 2009, 09:03 PM

ok so $<br /> \left(4 + x^2\right)^{\frac{1}{2}}<br />$ means to mulitply the inside (4+x^2) by 1/2 if 4 and x are not products of each other?

**Stroodle** · December 8th 2009, 09:06 PM

Because that is just the square root of each term, not the square root of both the terms added together; for example:

$\sqrt{3+1}\neq\sqrt{3}+\sqrt{1}$

It equals 2.

**HallsofIvy** · December 9th 2009, 03:52 AM

Originally Posted by am1

if i had squareroot(4+x^2) why can't i simplify it down to (2+x), why isn't that legal?

It isn't "legal" because it gives the wrong answer! $\sqrt{4+x^2}$ is NOT 2+ x because $(2+x)^2= (2+x)(2+x)= 4+ 4x+ x^2$ is not equal to $4+ x^2$ .

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