#dc, 9

    0?dvd*-^p

Outputs 0 for truthy and an integer > 0 for falsey.

[Try it online][1].

    0            # Push zero.  Stack: [ 0 ]
     ?           # Push input.  Stack: [ n, 0 ]
      dv         # duplicate and take integer square root.  Stack: [ ⌊√n⌋, n, 0 ]
        d        # duplicate.  Stack: [ ⌊√n⌋, ⌊√n⌋, n, 0 ]
         *       # multiply.  Stack: [ ⌊√n⌋², n, 0 ]
          -      # take difference. Stack: [ n-⌊√n⌋², 0 ]
           ^     # 0 to power of the result.  Stack: [ 0^(n-⌊√n⌋²) ]
            p    # print.

Note `dc`'s `^` exponentiation command gives 0<sup>0</sup>=1 and 0<sup>n</sup>=0, where n>0.

  [1]: https://tio.run/##RYtBCsIwEADvfcVQlIIQaDW0AUF/ItTslvaSlCb05N@jCOIcZ5jnmOYyxY2sKfsxKUugpaO3OMe5s4N1l94OVyRWfFi3JeSJ@pgwN2oOv/Nb1c/xr3ghHqM0pb3LLifzWEtTSQxa3g