To solve the expression [tex]\(\sqrt{2} + \frac{1}{2} - \sqrt{5}\)[/tex], we need to evaluate each of the components individually and then combine them according to the given arithmetic operations.
1. Evaluate [tex]\(\sqrt{2}\)[/tex]:
The square root of 2 is approximately:
[tex]\[
\sqrt{2} \approx 1.4142135623730951
\][/tex]
2. Evaluate [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\frac{1}{2} = 0.5
\][/tex]
3. Evaluate [tex]\(\sqrt{5}\)[/tex]:
The square root of 5 is approximately:
[tex]\[
\sqrt{5} \approx 2.23606797749979
\][/tex]
4. Combine the results:
Now we add and subtract these components as specified in the original expression:
[tex]\[
\sqrt{2} + \frac{1}{2} - \sqrt{5}
\][/tex]
Substitute the numerical values:
[tex]\[
1.4142135623730951 + 0.5 - 2.23606797749979
\][/tex]
5. Perform the addition and subtraction:
[tex]\[
1.4142135623730951 + 0.5 = 1.9142135623730951
\][/tex]
[tex]\[
1.9142135623730951 - 2.23606797749979 = -0.32185441512669466
\][/tex]
Therefore, the value of the expression [tex]\(\sqrt{2} + \frac{1}{2} - \sqrt{5}\)[/tex] is:
[tex]\[
-0.32185441512669466
\][/tex]
