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Algebra

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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 -

    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 -

    Thank you :D That really cleared it up! I never had anyone explain that concept so well before.

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