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I had the textbook question:

What is the degree of the following expression:

$x^2\sqrt{y-5}$

Would it be 2.5, since it would be the sum of the exponents of $x$ (2) and $y$ (.5, I think)? Or is this wrong?

The confusing part is the exponent of $y$, because it is not $\sqrt{y}$, but $\sqrt{y-5}$. Would $y$'s exponent still be $y^{1/2}$?

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  • $\begingroup$ but this is not a polynomial $\endgroup$ Commented Jan 4, 2016 at 16:57
  • $\begingroup$ You are dealing with homogeneous functions? $\endgroup$
    – Albert
    Commented Jan 4, 2016 at 16:59
  • $\begingroup$ @Dr.SonnhardGraubner Sorry, the question included other polynomials, and you would find the degree of this the same way as the largest degree of a polynomial $\endgroup$ Commented Jan 4, 2016 at 17:02
  • $\begingroup$ @Albert Sorry, what is a homogenous function? This is simply a monomial, a single-termed expression. $\endgroup$ Commented Jan 4, 2016 at 17:03
  • $\begingroup$ A function $f(x,y)$ is said to be homogeneous with degree $n$ if $f(\lambda x,\lambda y)=\lambda^{n}f(x,y)$. $\endgroup$
    – Albert
    Commented Jan 4, 2016 at 17:10

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