Posted by **Adriana** on Wednesday, October 28, 2009 at 4:39pm.

I had to solve the function g of f where f is x^2+1 and g is sq. root of x. I wrote this out as the sq. root of x^2+1. The ^2 and the sq. root canceled each other out, so I was left with x + sq. root of 1. But my book got sq. root of x^2+1. Was the further reducing I did acceptable or inaccurate?

- Algebra -
**jim**, Wednesday, October 28, 2009 at 6:21pm
You can't separate the added parts and take the square root of each. (You could if they were multiplied, but not if added.)

I will show a counterexample.

You were looking at sqrt(x^2+1).

Consider this example - let x=3, then we have :

sqrt(3^2+1) = sqrt(9+1) = sqrt(10)

Now, you would have said that this was equal to

3 + sqrt(1) = 4.

But 4 is not the square root of 10.

We can get in deeper about why your approach doesn't work if you like, but this counterexample is enough to show it's not true.

- Algebra -
**Adriana**, Wednesday, October 28, 2009 at 10:47pm
Thank you :D That really cleared it up! I never had anyone explain that concept so well before.

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