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\frac{1}{16}\left(5+\sqrt{1+24}\right)
Add 1 and 4 to get 5.
\frac{1}{16}\left(5+\sqrt{25}\right)
Add 1 and 24 to get 25.
\frac{1}{16}\left(5+5\right)
Calculate the square root of 25 and get 5.
\frac{1}{16}\times 10
Add 5 and 5 to get 10.
\frac{10}{16}
Multiply \frac{1}{16} and 10 to get \frac{10}{16}.
\frac{5}{8}
Reduce the fraction \frac{10}{16} to lowest terms by extracting and canceling out 2.