Question

write down the mode of the first 12 digits of \\(\sqrt{5}\\)

\\\sqrt{5} = 2.23606797749...\\

Explanation:

Identify the first 12 digits of \(\sqrt{5}\)

The given expansion is \(\sqrt{5} = 2.23606797749\dots\)
The first 12 digits are:
\(2, 2, 3, 6, 0, 6, 7, 9, 7, 7, 4, 9\)

Count the frequency of each digit

We count how many times each digit appears in the list:

• Digit \(0\): 1 time
• Digit \(2\): 2 times
• Digit \(3\): 1 time
• Digit \(4\): 1 time
• Digit \(6\): 2 times
• Digit \(7\): 3 times
• Digit \(9\): 2 times

Determine the mode

The mode is the value that appears most frequently.
The digit \(7\) appears 3 times, which is more than any other digit.

Answer:

7