To find the square root of [tex]\( 5 \frac{1}{16} \)[/tex], let's go through the process step by step.
1. Convert the mixed number to an improper fraction or decimal:
The mixed number [tex]\( 5 \frac{1}{16} \)[/tex] can be written as a single number. Since [tex]\( 5 \frac{1}{16} = 5 + \frac{1}{16} \)[/tex], we need to add these two parts together.
The fraction [tex]\( \frac{1}{16} \)[/tex] is already in its simplest form. When we add it to 5, we get:
[tex]\[
5 + \frac{1}{16} = 5.0625
\][/tex]
2. Calculate the square root of this value:
Now that we have the value 5.0625, let's find its square root. The square root of 5.0625 is:
[tex]\[
\sqrt{5.0625} = 2.25
\][/tex]
So, the square root of [tex]\( 5 \frac{1}{16} \)[/tex] is [tex]\( 2.25 \)[/tex].
Thus, the final answer is [tex]\(\sqrt{5 \frac{1}{16}} = 2.25\)[/tex].
