Answer :
Sure, let's go through the steps to solve the expression \(\sqrt{2} + \frac{1}{2} - \sqrt{5}\) in detail.
1. Calculate the value of \(\sqrt{2}\):
The square root of 2 is approximately \(1.4142135623730951\).
2. Evaluate \(\frac{1}{2}\):
Since \(\frac{1}{2}\) is a simple fraction, its value is \(0.5\).
3. Calculate the value of \(\sqrt{5}\):
The square root of 5 is approximately \(2.23606797749979\).
4. Substitute the values into the expression:
Replace \(\sqrt{2}\) with \(1.4142135623730951\) and \(\sqrt{5}\) with \(2.23606797749979\) in the original expression:
[tex]\[ 1.4142135623730951 + 0.5 - 2.23606797749979 \][/tex]
5. Perform the addition and subtraction:
- First, add \(1.4142135623730951\) and \(0.5\):
[tex]\[ 1.4142135623730951 + 0.5 = 1.9142135623730951 \][/tex]
- Next, subtract \(2.23606797749979\) from the result:
[tex]\[ 1.9142135623730951 - 2.23606797749979 = -0.32185441512669466 \][/tex]
So, the value of the expression [tex]\(\sqrt{2} + \frac{1}{2} - \sqrt{5}\)[/tex] is approximately [tex]\(-0.32185441512669466\)[/tex].
1. Calculate the value of \(\sqrt{2}\):
The square root of 2 is approximately \(1.4142135623730951\).
2. Evaluate \(\frac{1}{2}\):
Since \(\frac{1}{2}\) is a simple fraction, its value is \(0.5\).
3. Calculate the value of \(\sqrt{5}\):
The square root of 5 is approximately \(2.23606797749979\).
4. Substitute the values into the expression:
Replace \(\sqrt{2}\) with \(1.4142135623730951\) and \(\sqrt{5}\) with \(2.23606797749979\) in the original expression:
[tex]\[ 1.4142135623730951 + 0.5 - 2.23606797749979 \][/tex]
5. Perform the addition and subtraction:
- First, add \(1.4142135623730951\) and \(0.5\):
[tex]\[ 1.4142135623730951 + 0.5 = 1.9142135623730951 \][/tex]
- Next, subtract \(2.23606797749979\) from the result:
[tex]\[ 1.9142135623730951 - 2.23606797749979 = -0.32185441512669466 \][/tex]
So, the value of the expression [tex]\(\sqrt{2} + \frac{1}{2} - \sqrt{5}\)[/tex] is approximately [tex]\(-0.32185441512669466\)[/tex].
