Let's solve this problem step-by-step.
First, we are given the value of [tex]\( a \)[/tex]:
[tex]\[ a = 3 - 2 \sqrt{2} \][/tex]
Next, we need to find the square root of [tex]\( a \)[/tex]:
[tex]\[ \sqrt{a} \][/tex]
From the given information, we know that:
[tex]\[ a = 0.1715728752538097 \][/tex]
Taking the square root of [tex]\( a \)[/tex], we get:
[tex]\[ \sqrt{a} = 0.4142135623730948 \][/tex]
Now, we need to find the value of [tex]\(\frac{1}{\sqrt{2}}\)[/tex]:
[tex]\[ \frac{1}{\sqrt{2}} = \frac{1}{1.4142135623730951} = 0.7071067811865475 \][/tex]
Finally, we need to compute:
[tex]\[ \sqrt{a} - \frac{1}{\sqrt{2}} \][/tex]
Using the values we have:
[tex]\[ 0.4142135623730948 - 0.7071067811865475 = -0.29289321881345265 \][/tex]
Thus, the value of [tex]\(\sqrt{a} - \frac{1}{\sqrt{2}}\)[/tex] is:
[tex]\[ -0.29289321881345265 \][/tex]
