Ein angeordneter Körper K {\displaystyle {}K} enthalte die Wurzeln 2 3 {\displaystyle {}{\sqrt[{3}]{2}}} und 2 7 {\displaystyle {}{\sqrt[{7}]{2}}} . Zeige, dass K {\displaystyle {}K} auch 2 21 {\displaystyle {}{\sqrt[{21}]{2}}} enthält.
![{\displaystyle {}{\sqrt[{3}]{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7045b852bf103b0f878521c0aa7b5b5e59cc2e72)
![{\displaystyle {}{\sqrt[{7}]{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8923d863a9eb5a82c65ac8a8acddb2b136c39d8a)
![{\displaystyle {}{\sqrt[{21}]{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9302bb2f621252b82b74ede11c5cd9419adcb869)