To find the square root of 7, denoted by [tex]\(\sqrt{7}\)[/tex], we look for a number which, when multiplied by itself, yields 7.
The square root of a number [tex]\(x\)[/tex] can be written as [tex]\(\sqrt{x}\)[/tex]. In this case, [tex]\(x = 7\)[/tex], so we are seeking [tex]\(\sqrt{7}\)[/tex].
Let's denote [tex]\(\sqrt{7}\)[/tex] as [tex]\(y\)[/tex]. Therefore, by definition, we have:
[tex]\[ y \times y = 7 \][/tex]
or
[tex]\[ y^2 = 7 \][/tex]
By taking the square root on both sides of the equation [tex]\(y^2 = 7\)[/tex], you isolate [tex]\(y\)[/tex]:
[tex]\[ y = \sqrt{7} \][/tex]
To give the numerical value of [tex]\(\sqrt{7}\)[/tex], we rely on advanced mathematical methods or computational tools that provide a precise value.
Thus, the value of [tex]\(\sqrt{7}\)[/tex] is approximately:
[tex]\[ \sqrt{7} \approx 2.6457513110645907 \][/tex]
This is the square root of 7 rounded to several decimal places, representing a more accurate result.
