R1 – Roots – Expressions

This post examines some examples of the full roots of expressions in R1. Calculate the full root as the root of the Counter times the root of the Unitary. 

Examples

• √(x?^?) = √x*√(1‡x^‡x )
  • For example where x = 16^{^}:
    • √(16^{^}) = √16*√1^{^} = 4*1^{^} = 4^{^} or
    • √(16^{^}) = √16*√1^{^} = 4*1^v = 4^v

• √(2x² ) = √2*√x²*√(1‡x^‡x) = x√2*√(1‡x^‡x)
  • For example where x = 3^{^}:
    • √(2*3^{^2} ) = √(18^{^}) = √18*√1^{^} = 3√2*1^{^} = 3√2^{^} or
      • = 3√2*1^v = 3√2^v

• √((x + 1^{^}/x)² + ^–4(x + 1^v/x))
  • = √(x² + 2^{^} + 1^{^}/x²  + ^–4x + 4^{^}/x) 
  • For example where x = 3^{^}:
    • = √((3^{^}+ 1^{^}/3^{^})² + ^–4(3^{^} + 1^v/3^{^})) = √((10/3^{^})² + ^–4(8/3^{^}))
      • = √(100/9^{^} + 32/3^v)
      • = √(4/9^{^}) = 0.667^{^} or 0.667^v
    • Or = √(3^{^2} + 2^{^} + 1^{^}/3^{^2}  + ^–4*3^{^} + 4^{^}/3^{^})
      • = √(9^{^}+ 2^{^} + 1/9^{^}  + 12^v + 4/3^{^})
      • = √(4/9^{^}) = 0.667^{^} or 0.667^v

• Calculate the root of the last expression directly as:
  • √((x^{^} + 1^{^}/x)² + ^–4(x^{^} + 1^v/x))
    • = √((3^{^} + 1^{^}/3^{^})² + ^–4(3^{^} + 1^v/3^{^}))
    • = √(3.333^{^2} + ^–4(2.666^{^})
    • = √(11.11^{^} + 10.664^v)
    • = √(0.446^{^}) = 0.667^{^} or 0.667^v

Conclusion

Our online calculator can help with the calculation of the roots of R1 expressions.

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