To solve [tex]\(\sqrt{13}\)[/tex], we are looking for a number which, when squared, equals 13.
The square root function is used to find such a number. Not all square roots of numbers are integers; frequently, they are irrational numbers which cannot be exactly expressed as simple fractions but can be represented as decimal numbers to a certain degree of precision.
For [tex]\(\sqrt{13}\)[/tex]:
1. We recognize that [tex]\(13\)[/tex] is not a perfect square, so its square root will not be an integer.
2. The nearest perfect squares surrounding 13 are [tex]\(9\)[/tex] ([tex]\(3^2\)[/tex]) and [tex]\(16\)[/tex] ([tex]\(4^2\)[/tex]).
3. Hence, [tex]\(\sqrt{13}\)[/tex] is between 3 and 4.
4. Calculating more precisely, [tex]\(\sqrt{13} \approx 3.605551275463989\)[/tex].
Thus, [tex]\(\sqrt{13} \approx 3.605551275463989\)[/tex]. This result indicates that 3.605551275463989 squared is approximately equal to 13.
