Lösung 3.1:8b

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If we write the numbers in power form,


\displaystyle \sqrt{7}=7^{{1}/{2}\;} and \displaystyle 7=7^{1}


it becomes clear that \displaystyle 7 is larger than \displaystyle \sqrt{7}, because both numbers have the same base, \displaystyle 7, which is larger than \displaystyle 1 and the exponent \displaystyle 1 is greater than \displaystyle {1}/{2}\;.