Sure, let's evaluate the expression [tex]\( \sqrt{2 \frac{9}{16}} \)[/tex] step by step.
1. Convert the Mixed Number to an Improper Fraction:
The given mixed number is [tex]\( 2 \frac{9}{16} \)[/tex].
- First, convert the whole number part (2) and the fractional part ([tex]\(\frac{9}{16}\)[/tex]) into an improper fraction:
[tex]\[
\text{Numerator} = 2 \times 16 + 9
\][/tex]
[tex]\[
\text{Numerator} = 32 + 9 = 41
\][/tex]
So, the improper fraction is:
[tex]\[
\frac{41}{16}
\][/tex]
2. Rewrite the Expression:
Now the expression becomes:
[tex]\[
\sqrt{\frac{41}{16}}
\][/tex]
3. Calculate the Value Inside the Square Root:
To simplify the square root of a fraction, we divide the numerator by the denominator:
[tex]\[
\frac{41}{16} = 2.5625
\][/tex]
4. Calculate the Square Root:
Now, we need to find the square root of [tex]\( 2.5625 \)[/tex]:
[tex]\[
\sqrt{2.5625} \approx 1.6007810593582121
\][/tex]
Therefore, the value of [tex]\( \sqrt{2 \frac{9}{16}} \)[/tex] is approximately [tex]\( 1.6007810593582121 \)[/tex].
