Step 1 :Given the expression \((\sqrt{2}+\sqrt{3})^{2}\)
Step 2 :We can simplify this using the formula for the square of a binomial, which is \((a+b)^2 = a^2 + 2ab + b^2\). Here, \(a\) is \(\sqrt{2}\) and \(b\) is \(\sqrt{3}\)
Step 3 :Substituting \(a\) and \(b\) into the formula, we get \((\sqrt{2})^2 + 2(\sqrt{2})(\sqrt{3}) + (\sqrt{3})^2\)
Step 4 :Solving this, we get \(2 + 2\sqrt{6} + 3\)
Step 5 :Combining like terms, we get \(5 + 2\sqrt{6}\)
Step 6 :\(\boxed{5 + 2\sqrt{6}}\) is the final answer