To find the value of [tex]\(\sqrt{2}\)[/tex], which is the square root of 2, we start by understanding what we're trying to determine: a number that, when multiplied by itself, equals 2.
1. The square root function is denoted by the radical symbol √. Therefore, [tex]\(\sqrt{2}\)[/tex] asks for a number which solves the equation [tex]\(x^2 = 2\)[/tex].
2. Recognizing that 2 is not a perfect square (since there is no whole number whose square is exactly 2), we must look for an approximation of this irrational number.
3. The value of [tex]\(\sqrt{2}\)[/tex] is approximately [tex]\(1.4142135623730951\)[/tex].
Hence,
[tex]\[
\sqrt{2} \approx 1.4142135623730951
\][/tex]
