Question

question
express the product $\left(\sqrt{5}+\sqrt{2}\
ight)\left(\sqrt{5}+\sqrt{2}\
ight)$ in simplest form.

Explanation:

Step1: Recognize perfect square

$(\sqrt{5}+\sqrt{2})(\sqrt{5}+\sqrt{2})=(\sqrt{5}+\sqrt{2})^2$

Step2: Apply square of sum formula

Recall $(a+b)^2=a^2+2ab+b^2$, so:
$(\sqrt{5})^2 + 2(\sqrt{5})(\sqrt{2}) + (\sqrt{2})^2$

Step3: Simplify each term

$\sqrt{5}^2=5$, $\sqrt{2}^2=2$, $2(\sqrt{5})(\sqrt{2})=2\sqrt{10}$

Step4: Combine constant terms

$5 + 2 + 2\sqrt{10}$

Answer:

$7 + 2\sqrt{10}$