From Förberedande kurs i matematik 1

Since \displaystyle 2.5^{2}=2.5\centerdot 2.5=6.25, then \displaystyle 2.5=\sqrt{6.25}, and then we see that \displaystyle \sqrt{7} is greater than 2.5 since \displaystyle 7^{{1}/{2}\;}>6.25^{{1}/{2}\;}