To find the value of the expression [tex]\(\frac{\sqrt{14.9 - 1.7}}{(6.3 + 0.07)^2}\)[/tex], follow these detailed steps:
1. Calculate the numerator:
[tex]\[
14.9 - 1.7 = 13.2
\][/tex]
Now, find the square root of [tex]\(13.2\)[/tex]:
[tex]\[
\sqrt{13.2} \approx 3.6331804249169903
\][/tex]
2. Calculate the denominator:
[tex]\[
6.3 + 0.07 = 6.37
\][/tex]
Next, square this value:
[tex]\[
(6.37)^2 = 40.5769
\][/tex]
3. Divide the numerator by the denominator:
[tex]\[
\frac{3.6331804249169903}{40.5769} \approx 0.08953814670211352
\][/tex]
Therefore, the value of the given expression is approximately [tex]\(0.08953814670211352\)[/tex].
