Sure, let's explore the solution to the question of finding the value of [tex]\(\sqrt{2}\)[/tex].
[tex]\(\sqrt{2}\)[/tex] is the positive number that, when multiplied by itself, gives the product 2. In other words, it solves the equation:
[tex]\[
x^2 = 2
\][/tex]
To find [tex]\(\sqrt{2}\)[/tex], we recognize that this is known as a special irrational number. It's not possible to express it as a fraction of two integers, and its decimal representation goes on forever without repeating. We often refer to it as approximately 1.414, but the exact value extends to more decimal places.
The value of [tex]\(\sqrt{2}\)[/tex] can be approximated to a high degree of precision. From our calculations, we find that:
[tex]\[
\sqrt{2} \approx 1.4142135623730951
\][/tex]
Therefore, the value of [tex]\(\sqrt{2}\)[/tex], when expressed in decimal form to sixteen decimal places, is:
[tex]\[
\boxed{1.4142135623730951}
\][/tex]
