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For how many real values of x is \(\sqrt{54 - \sqrt{x}}\) an integer?

 Jun 27, 2020
 #1
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look for perfect squares less than 54     49   36   25   16  9   4   1  0

   subtract them from 54 to see if any results in a perfect square

54-49 = 5     so if sqrt x = 5     would be one  x = 25

54-36=18             sqrtx=18                              x = 324

            29                                                               841

            38                                                               1444

            45                                                              2025

            50                                                              2500    

            53                                                              2809      

            54                                                               2916         eight values of x

 Jun 27, 2020
edited by ElectricPavlov  Jun 27, 2020

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