Question

simplify (root 5 + root 2)² ​

Answer 1

$(\sqrt{5} + \sqrt{2})^2 \\\\\ \implies (\sqrt{5})^2 + 2(\sqrt{5})(\sqrt{2}) + (\sqrt{2})^2 \\\\\ \implies 5 + 2\sqrt{10} + 2$

Answer 2

$\red{\boxed{\boxed{ 7 + 2 \sqrt{10} }}}$

Step-by-step explanation:

simplify (root 5 + root 2)²

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

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

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

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

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

$= 7 + 2 \sqrt{10}$

${\purple{\boxed{ {\mathfrak{\underline{\purple{ @11177420 }}}} }}}$