Question

question
express the product $\left(\sqrt{3}+\sqrt{2}\
ight)\left(\sqrt{3}+\sqrt{2}\
ight)$ in simplest form.

Explanation:

Step1: Recognize perfect square

$(\sqrt{3}+\sqrt{2})(\sqrt{3}+\sqrt{2}) = (\sqrt{3}+\sqrt{2})^2$

Step2: Apply square of sum formula

Recall $(a+b)^2=a^2+2ab+b^2$, where $a=\sqrt{3}$, $b=\sqrt{2}$
$(\sqrt{3})^2 + 2(\sqrt{3})(\sqrt{2}) + (\sqrt{2})^2$

Step3: Simplify each term

$\sqrt{3}^2=3$, $\sqrt{2}^2=2$, $2(\sqrt{3})(\sqrt{2})=2\sqrt{6}$
$3 + 2\sqrt{6} + 2$

Step4: Combine constant terms

$3+2=5$
$5 + 2\sqrt{6}$

Answer:

$5 + 2\sqrt{6}$