Question

escreva na forma mais simples possivel cada uma das expressões a seguir
$\sqrt{3 } + \sqrt{75 } - \sqrt{12} \\ \\ \sqrt{11} + \sqrt{44} - 2 \sqrt{99} + \sqrt{176}$
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Answer 1

a)

$\sqrt{3}+\sqrt{75}-\sqrt{12}~=~\sqrt{3}+\sqrt{3~.~5~.~5}-\sqrt{3~.~2~.~2}~=\\\\\\=~\sqrt{3}+\sqrt{3~.~5^2}-\sqrt{3~.~2^2}~=~\sqrt{3}+5\sqrt{3}-2\sqrt{3}~=\\\\\\=~\boxed{4\sqrt{3}}$

b)

$\sqrt{11}+\sqrt{44}-2\sqrt{99}+\sqrt{176}~=\\\\\\=~\sqrt{11}+\sqrt{2~.~2~.~11}-2\sqrt{3~.~3~.~11}+\sqrt{2~.~2~.~2~.~2~.~11}~=\\\\\\=~\sqrt{11}+\sqrt{2^2~.~11}-2\sqrt{3^2~.~11}+\sqrt{2^2~.~2^2~.~11}~=\\\\\\=~\sqrt{11}+2\sqrt{11}-2~.~3\sqrt{11}+2~.~2\sqrt{11}\\\\\\=~\sqrt{11}+2\sqrt{11}-6\sqrt{11}+4\sqrt{11}\\\\\\=~\boxed{\sqrt{11}}$