why does the scientific calculator show that (2 1/2) squared is 1, when it is actually 6 1/4?
Because, you are probably doing something wrong. Enter 2 1/2 as 2.5 and press x^2 key followed by = sign to get your answer.
+1904 Two ways to solve this.
The long way:
\((2+\frac{1}{2})^2\)
\((2+\frac{1}{2})(2+\frac{1}{2})\)
\(2\times2+2\times\frac{1}{2}+2\times\frac{1}{2}+\frac{1}{2}\times\frac{1}{2}\)
\(4+2\times\frac{1}{2}+2\times\frac{1}{2}+\frac{1}{2}\times\frac{1}{2}\)
\(4+\frac{2}{2}+2\times\frac{1}{2}+\frac{1}{2}\times\frac{1}{2}\)
\(4+1+2\times\frac{1}{2}+\frac{1}{2}\times\frac{1}{2}\)
\(4+1+\frac{2}{2}+\frac{1}{2}\times\frac{1}{2}\)
\(4+1+1+\frac{1}{2}\times\frac{1}{2}\)
\(4+1+1+\frac{1}{4}\)
\(5+1+\frac{1}{4}\)
\(6+\frac{1}{4}\)
\(\frac{24}{4}+\frac{1}{4}\)
\(\frac{25}{4}\)
\(6\frac{1}{4}\)
\(6.25\)
The short way:
\((2+\frac{1}{2})^2\)
\((\frac{4}{2}+\frac{1}{2})^2\)
\((\frac{5}{2})^2\)
\(\frac{5^2}{2^2}\)
\(\frac{25}{2^2}\)
\(\frac{25}{4}\)
\(6\frac{1}{4}\)
\(6.25\)
