Question

(root2+root3)(root2+root5) explain step by step​

Answer 1

Answer:

$\ \purple{ \boxed{{\sf{{⋆⫷❥ᴀ᭄n §₩ΣR⫸⋆}}}}}$

$\huge\sf \underline{ \ given: }$

$\bf \: ( \sqrt{2} + \sqrt{3} )( \sqrt{2} + \sqrt{5} )$

$\huge\sf \underline{ \ to \: find: }$

$\bf \: product \: obtained$

$\huge\sf \underline{ \ solution: }$

$\sf \underline{as \: we \: know \: that \ \: : }$

$\sf (x + a)(x + b) \ \: : \\ \sf \to {x}^{2} + x(a + b) + ab$

$\sf \underline{here \ \: : }$

$\sf \: x \ \: : \: \sqrt{2}$

$\sf \: a \ \: : \: \sqrt{3}$

$\sf \: b \ \: : \: \sqrt{5}$

$\sf \underline{let \: us \: solve \ \: : }$

$\sf \to( \sqrt{2} + \sqrt{3} )( \sqrt{2} + \sqrt{5} )$

$\sf \to { \sqrt{2} }^{2} + \sqrt{2} ( \sqrt{2} + \sqrt{5}) + \sqrt{2} \times \sqrt{5}$

$\sf \to2 + 2 + 2 \sqrt{5} + \sqrt{10}$

$\sf \to \: 4 + 2 \sqrt{5} + \sqrt{10}$