Comparison of Two Radical Expressions*

Problem:

Which is larger? for which x and y? Prove.

Note: If we assumed that the order is the same for all x and y, then we could test a particular point (x,y) such as (0,0). For (0,0) the first equation has z = 4 and for the second equation z = 2. Thus, at (0,0) the first is larger than the second. The problem becomes

Prove the first is greater than the second for all x and y.

Here is a GCF graph of the two equations:

Click HERE for a link to the GCF file.

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*Problem suggested by William Sergeant, Central Michigan University.