Question

Simplify
(√3+4) (2+√5)​

Answer 1

$Given \: (\sqrt{3} + 4 )( 2 + \sqrt{5})$

$= \sqrt{3}( 2 + \sqrt{5}) + 4( 2 +\sqrt{5})$

$= \sqrt{3}\times 2 + \sqrt{2} \times \sqrt{5} + 4\times 2 + 4 \times \sqrt{5}$

$=2 \sqrt{3} + \sqrt{10} + 8 + 4 \sqrt{5}$

$=8 + 2 \sqrt{3} + \sqrt{10} + 4 \sqrt{5}$

Therefore.,

$\red{ (\sqrt{3} + 4 )( 2 + \sqrt{5})}$

$\green {=8 + 2 \sqrt{3} + \sqrt{10} + 4 \sqrt{5} }$

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Answer 2

${\tt{\purple{\underline{\underline{\huge{Answer:}}}}}}$

${\red{\boxed{Given}}}$

$(\sqrt{3} + 4 )( 2 + \sqrt{5})$

$\sf\implies \sqrt{3}( 2 + \sqrt{5}) + 4( 2 +\sqrt{5})$

$\sf\implies \sqrt{3}\times 2 + \sqrt{2} \times \sqrt{5} + 4\times 2 + 4 \times \sqrt{5}$

$\sf\implies 2 \sqrt{3} + \sqrt{10} + 8 + 4 \sqrt{5}$

$\sf\implies 8 + 2 \sqrt{3} + \sqrt{10} + 4 \sqrt{5}$

$\sf\implies (\sqrt{3} + 4 )( 2 + \sqrt{5})$

$\sf\implies 8 + 2 \sqrt{3} + \sqrt{10} + 4 \sqrt{5}$

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